FRANK Solutions for Class 9 Maths Chapter 5 - Factorisation
Achieve high marks with the support of Frank Solutions for ICSE Class 9 Mathematics Chapter 5 Factorisation. Prepared by TopperLearning’s experts, the solutions will help you understand how to factorise mathematical expressions by removing the common factors.
Also, learn the method of using the difference of two squares to factorise the given data. Explore ICSE Class 9 Maths Frank textbook solutions any time online on our online education portal. Additionally, with the help of our concept videos and online practice tests designed by subject experts, you can get ahead in your Maths learning.
Chapter 5 - Factorisation Exercise Ex. 5.1
Factorise the following by taking out the common factors:
4x2y3 - 6x3y2 - 12xy2
Factorise the following by taking out the common factors:
5a(x2 - y2) + 35b(x2 - y2)
Factorise the following by taking out the common factors:
2x5y + 8x3y2 - 12x2y3
Factorise the following by taking out the common factors:
12a3 + 15a2b - 21ab2
Factorise the following by taking out the common factors:
24m4n6 + 56m6n4 - 72m2n2
Factorise the following by taking out the common factors:
(a - b)2 -2(a - b)
Factorise the following by taking out the common factors:
2a(p2 + q2) + 4b(p2 + q2)
Factorise the following by taking out the common factors:
81(p + q)2 -9p - 9q
Factorise the following by taking out the common factors:
(mx + ny)2 + (nx - my)2
Factorise the following by taking out the common factors:
36(x + y)3 - 54(x + y)2
Factorise the following by taking out the common factors:
p(p2 + q2 - r2) + q(r2 - q2 -p2) - r(p2 + q2 - r2)
Factorise the following by grouping the terms:
15xy - 9x - 25y + 15
15xy - 9x - 25y + 15
= (15xy - 9x) - (25y + 15)
= 3x(5y - 3) - 5(5y - 3)
= (5y - 3)(3x - 5)
Factorise the following by grouping the terms:
15x2 + 7y - 3x - 35xy
15x2 + 7y - 3x - 35xy
= 15x2 - 3x - 35xy + 7y
= (15x2 - 3x) - (35xy - 7y)
= 3x(5x - 1) - 7y(5x - 1)
= (5x - 1)(3x - 7y)
Factorise the following by grouping the terms:
9 + 3xy + x2y + 3x
9 + 3xy + x2y + 3x
= 9 + 3xy + 3x + x2y
= (9 + 3xy) + (3x + x2y)
= 3(3 + xy) + y(3 + xy)
= (3 + xy)(3 + x)
Factorise the following by grouping the terms:
8(2a + b)2 - 8a -4b
8(2a + b)2 - 8a - 4b
= 8(2a + b)2 - (8a + 4b)
= 8(2a + b)2 - 4(2a + b)
= 4(2a + b)[2(2a + b) - 1]
= 4(2a + b)[4a + 2b - 1]
Factorise the following by grouping the terms:
x(x - 4)- x + 4
x(x - 4) - x + 4
= x(x - 4) - 1(x - 4)
= (x - 4)(x - 1)
Factorise the following by grouping the terms:
2m3 - 5n2 - 5m2n + 2mn
2m3 - 5n2 - 5m2n + 2mn
= 2m3 + 2mn - 5m2n - 5n2
= (2m3 + 2mn) - (5m2n + 5n2)
= 2m(m2 + n) - 5n(m2 + n)
= (m2 + n)(2m - 5n)
Factorise the following by grouping the terms:
4abx2 + 49aby2 + 14xy(a2 + b2)
4abx2 + 49aby2 + 14xy(a2 + b2)
= 4abx2 + 49aby2 + 14a2xy + 14b2xy
= (4abx2 + 14a2xy) + (14b2xy + 49aby2)
= 2ax(2bx + 7ay) + 7by(2bx + 7ay)
= (2bx + 7ay)(2ax + 7by)
Factorise the following by grouping the terms:
9x3 + 6x2y2 - 4y3 - 6xy
9x3 + 6x2y2 - 4y3 - 6xy
= 9x3 + 6x2y2 - 6xy - 4y3
= (9x3 + 6x2y2) - (6xy + 4y3)
= 3x2(3x + 2y2) - 2y(3x + 2y2)
= (3x + 2y2)(3x2 - 2y)
Factorise the following by grouping the terms:
3ax2 - 5bx2 + 9az2 + 6ay2 - 10by2 - 15bz2
3ax2 - 5bx2 + 9az2 + 6ay2 - 10by2 - 15bz2
= 3ax2 + 6ay2 + 9az2 - 5bx2 - 10by2 - 15bz2
= (3ax2 + 6ay2 + 9az2) - (5bx2 + 10by2 + 15bz2)
= 3a(x2 + 2y2 + 3z2) - 5b(x2 + 2y2 + 3z2)
= (x2 + 2y2 + 3z2)(3a - 5b)
Factorise the following by grouping the terms:
8x3 - 24x2y + 54xy2 -162y3
8x3 - 24x2y + 54xy2 - 162y3
= (8x3 - 24x2y) + (54xy2 - 162y3)
= 8x2(x - 3y) + 54y2(x - 3y)
= (x - 3y)(8x2 + 54y2)
Factorise the following by grouping the terms:
2a + b + 3c - d + (2a + b)3 + (2a + b)2(3c - d)
2a + b + 3c - d + (2a + b)3 + (2a + b)2(3c - d)
= (2a + b + 3c - d) + [(2a + b)3 + (2a + b)2(3c - d)]
= 1(2a + b + 3c - d) + (2a + b)2(2a + b + 3c - d)
= (2a + b + 3c - d)[1 + (2a + b)2]
Factorise the following by grouping the terms:
xy(a2 + 1) + a(x2 + y2)
xy(a2 + 1) + a(x2 + y2)
= a2xy + xy + ax2 + ay2
= (a2xy + ax2) + (ay2 + xy)
= ax(ay + x) + y(ay + x)
= (ay + x)(ax + y)
Factorise the following by grouping the terms:
p2x2 + (px2 + 1)x + p
p2x2 + (px2 + 1)x + p
= p2x2 + px3 + x + p
= (p2x2 + px3) + (p + x)
= px2(p + x) + 1(p + x)
= (p + x)(px2 + 1)
Factorise the following by grouping the terms:
x2 - (p + q)x + pq
x2 - (p + q)x + pq
= x2 - px - qx + pq
= (x2 - px) - (qx + pq)
= x(x - p) - q(x - p)
= (x - p)(x - q)
Factorise the following by grouping the terms:
Factorise the following by grouping the terms:
x + y + m(x + y)
x + y + m(x + y)
= (x + y) + m(x + y)
= (x + y)(1 + m)
Factorise the following by grouping the terms:
Factorise the following by grouping the terms:
2p(a2 - 2b2) -14p + (a2 - 2b2)2 - 7(a2 - 2b2)
2p(a2 - 2b2) - 14p + (a2 - 2b2)2 - 7(a2 - 2b2)
= 2p(a2 - 2b2) + (a2 - 2b2)2 - 14p - 7(a2 - 2b2)
= [2p(a2 - 2b2) + (a2 - 2b2)2] - [14p + 7(a2 - 2b2)]
= (a2 - 2b2)(2p + a2 - 2b2) - 7(2p + a2 - 2b2)
= (2p + a2 - 2b2)(a2 - 2b2 - 7)
Chapter 5 - Factorisation Exercise Ex. 5.2
Factorise the following by splitting the middle term:
x2 + 6x + 8
x2 + 6x + 8
= x2 + 4x + 2x + 8
= x(x + 4) + 2(x + 4)
= (x + 4)(x + 2)
Factorise the following by splitting the middle term:
x2 - 11x + 24
x2 - 11x + 24
= x2 - 8x - 3x + 24
= x(x - 8) - 3(x - 8)
= (x - 8)(x - 3)
Factorise the following by splitting the middle term:
x2 + 5x - 6
x2 + 5x - 6
= x2 + 6x - x - 6
= x(x + 6) - 1(x + 6)
= (x + 6)(x - 1)
Factorise the following by splitting the middle term:
p2- 12p - 64
p2 - 12p - 64
= p2 - 16p + 4p - 64
= p(p - 16) + 4(p - 16)
= (p - 16)(p + 4)
Factorise the following by splitting the middle term:
y2 - 2y - 24
y2 - 2y - 24
= y2 - 6y + 4y - 24
= y(y - 6) + 4(y - 6)
=(y - 6)(y + 4)
Factorise the following by splitting the middle term:
3x2 + 19x - 14
3x2 + 19x - 14
= 3x2 + 21x - 2x - 14
= 3x(x + 7) - 2(x + 7)
= (x + 7)(3x - 2)
Factorise the following by splitting the middle term:
15a2 - 14a - 16
15a2 - 14a - 16
= 15a2 - 24a + 10a - 16
= 3a(5a - 8) + 2(5a - 8)
= (5a - 8)(3a + 2)
Factorise the following by splitting the middle term:
12 + x - 6x2
12 + x - 6x2
= 12 + 9x - 8x - 6x2
= 3(4 + 3x) - 2x(4 + 3x)
= (4 + 3x)(3 - 2x)
Factorise the following by splitting the middle term:
7x2 + 40x - 12
7x2 + 40x - 12
= 7x2 + 42x - 2x - 12
= 7x(x + 6) - 2(x + 6)
= (x + 6)(7x - 2)
Factorise the following:
5x2 - 17xy + 6y2
5x2 - 17xy + 6y2
= 5x2 - 15xy - 2xy + 6y2
= 5x(x - 3y) - 2y(x - 3y)
= (x - 3y)(5x - 2y)
Factorise the following:
9x2 - 22xy + 8y2
9x2 - 22xy + 8y2
= 9x2 - 18xy - 4xy + 8y2
= 9x(x - 2y) - 4y(x - 2y)
= (x - 2y)(9x - 4y)
Factorise the following:
2x3 + 5x2y - 12xy2
2x3 + 5x2y - 12xy2
= 2x3 + 8x2y - 3x2y - 12xy2
= 2x2(x + 4y) - 3xy(x + 4y)
= (x + 4y)(2x2 - 3xy)
= (x + 4y)x(2x - 3y)
= x(x + 4y)(2x - 3y)
Factorise the following:
x2y2 + 15xy - 16
x2y2 + 15xy - 16
= x2y2 + 16xy - xy - 16
= xy(xy + 16) - 1(xy + 16)
= (xy + 16)(xy - 1)
Factorise the following:
(2p + q)2 - 10p - 5q - 6
(2p + q)2 - 10p - 5q - 6
= (2p + q)2 - (10p - 5q) - 6
= (2p + q)2 - 5(2p + q) - 6
= (2p + q)2 - 6(2p + q) + (2p + q) - 6
= (2p + q)(2p + q - 6) + 1(2p + q - 6)
= (2p + q - 6)(2p + q + 1)
Factorise the following:
y2 + 3y + 2 + by + 2b
y2 + 3y + 2 + by + 2b
= y2 + y + 2y + 2 + by + 2b
= y2 + y + by + 2y + 2 + 2b
= y(y + 1 + b) + 2(y + 1 + b)
= (y + 1 + b)(y + 2)
Factorise the following:
x3y3 - 8x2y2 + 15xy
x3y3 - 8x2y2 + 15xy
= x3y3 - 3x2y2 - 5x2y2 + 15xy
= x2y2(xy - 3) - 5xy(xy - 3)
= (xy - 3)(x2y2 - 5xy)
= (xy - 3)xy(xy - 5)
= xy(xy - 3)(xy - 5)
Factorise the following:
Factorise the following:
Factorise the following:
5(3x + y)2 + 6(3x + y) - 8
5(3x + y)2 + 6(3x + y) - 8
= 5(3x + y)2 + 10(3x + y) - 4(3x + y) - 8
= 5(3x + y)(3x + y + 2) - 4(3x + y + 2)
= (3x + y + 2)[5(3x + y) - 4]
Factorise the following:
5 - 4(a - b) - 12(a - b)2
5 - 4(a - b) - 12(a - b)2
= 5 - 10(a - b) + 6(a - b) - 12(a - b)2
= 5[1 - 2(a - b)] + 6(a - b)[1 - 2(a - b)]
= [5 + 6(a - b)][1 - 2(a - b)]
= (5 + 6a - 6b)(1 - 2a + 2b)
Factorise the following:
(3a - 2b)2 +3(3a - 2b) - 10
(3a - 2b)2 + 3(3a - 2b) - 10
= (3a - 2b)2 + 5(3a - 2b) - 2(3a - 2b) - 10
= (3a - 2b)(3a - 2b + 5) - 2(3a - 2b +5)
= (3a - 2b + 5)((3a - 2b - 2)
Factorise the following:
(a2 - 2a)2 - 23(a2 - 2a) + 120
(a2 - 2a)2 - 23(a2 - 2a) + 120
= (a2 - 2a)2 - 15(a2 - 2a) - 8(a2 - 2a) + 120
= (a2 - 2a)(a2 - 2a - 15) - 8(a2 - 2a - 15)
= (a2 - 2a - 15)(a2 - 2a - 8)
= (a2 - 5a + 3a - 15)(a2 - 4a + 2a - 8)
= [a(a - 5) + 3(a - 5)][a(a - 4) + 2(a - 4)]
= [(a - 5)(a + 3)][(a - 4)(a + 2)]
= (a - 5)(a + 3)(a - 4)(a + 2)
= (a + 2)(a + 3)(a - 4)(a - 5)
Factorise the following:
(x + 4)2 - 5xy - 20y - 6y2
(x + 4)2 - 5xy - 20y - 6y2
= (x + 4)2 - 5y(x + 4) - 6y2
= (x + 4)2 - 6y(x + 4) + y(x + 4) - 6y2
= (x + 4)(x + 4 - 6y) + y(x + 4 - 6y)
= (x + 4 - 6y)(x + 4 + y)
= (x - 6y + 4)(x + y + 4)
Factorise the following:
7(x - 2)2 - 13(x - 2) - 2
7(x - 2)2 - 13(x - 2) - 2
= 7(x - 2)2 - 14(x - 2) + (x - 2) - 2
= 7(x - 2)(x - 2 - 2) + 1(x - 2 - 2)
= 7(x - 2)(x - 4) + 1(x - 4)
= (x - 4)[7(x - 2) + 1]
= (x - 4)(7x - 14 + 1)
= (x - 4)(7x - 13)
Factorise the following:
12 - (y + y2)(8 - y - y2)
12 - (y + y2)(8 - y - y2)
= 12 - a(8 - a) [Taking y + y2 = a]
= 12 - 8a + a2
= 12 - 6a - 2a + a2
= 6(2 - a) - a(2 - a)
= (2 - a)(6 - a)
= [2 - (y + y2)][6 - (y + y2)]
= (2 - y - y2)(6 - y - y2)
= (2 - 2y + y - y2)(6 - 3y + 2y - y2)
= [2(1 - y) + y(1 - y)][3(2 - y) + y(2 - y)]
= [(1 - y)(2 + y)][(2 - y)(3 + y)]
= (1 - y)(2 + y)(2 - y)(3 + y)
= (y - 1)(y + 2)(y - 2)(y + 3)
Factorise the following:
(p2 + p)2 - 8(p2 + p) + 12
(p2 + p)2 - 8(p2 + p) + 12
= (p2 + p)2 - 6(p2 + p) - 2(p2 + p) + 12
= (p2 + p)(p2 + p - 6) - 2(p2 + p - 6)
= (p2 + p - 6)(p2 + p - 2)
= (p2 + 3p - 2p - 6)(p2 + 2p - p - 2)
= [p(p + 3) - 2(p + 3)][p(p + 2) - 1(p + 2)]
= [(p + 3)(p - 2)][(p + 2)(p - 1)]
= (p + 3)(p - 2)(p + 2)(p - 1)
Factorise the following:
(y2 - 3y)(y2 - 3y + 7) + 10
(y2 - 3y)(y2 - 3y + 7) + 10
= a(a + 7) + 10 [taking (y2 - 3y) = a]
= a2 + 7a + 10
= a2 + 5a + 2a + 10
= a(a + 5) + 2(a + 5)
= (a + 5)(a + 2)
= (y2 - 3y + 5)(y2 - 3y + 2)
= (y2 - 3y + 5)(y2 - 2y - y + 2)
= (y2 - 3y + 5)[y(y - 2) - 1(y - 2)]
= (y2 - 3y + 5)[(y - 2)(y - 1)]
= (y - 1)(y - 2)(y2 - 3y + 5)
Factorise the following:
(t2 - t)(4t2 - 4t - 5) - 6
(t2 - t)(4t2 - 4t - 5) - 6
= (t2 - t)[4(t2 - t) - 5] - 6
= a[4a - 5] - 6 [Taking (t2 - t) = a]
= 4a2 - 5a - 6
= 4a2 - 8a + 3a - 6
= 4a(a - 2) + 3(a - 2)
= (a - 2)(4a + 3)
= (t2 - t - 2)[4(t2 - t) + 3]
= (t2 - 2t + t - 2)(4t2 - 4t + 3)
= [t(t - 2) + 1(t - 2)](4t2 - 4t + 3)
= [(t - 2)(t + 1)](4t2 - 4t + 3)
= (t + 1)(t - 2)(4t2 - 4t + 3)
Factorise the following:
12(2x - 3y)2 - 2x + 3y - 1
12(2x - 3y)2 - 1(2x - 3y) - 1
= 12a2 - a - 1 [Taking (2x - 3y) = a]
= 12a2 - 4a + 3a - 1
= 4a(3a - 1) + 1(3a - 1)
= (3a - 1)(4a + 1)
= [3(2x - 3y) - 1][4(2x - 3y) + 1]
= (6x - 9y - 1)(8x - 12y + 1)
Factorise the following:
6 - 5x + 5y + (x - y)2
6 - 5x + 5y + (x - y)2
= 6 - 5(x - y) + (x - y)2
= 6 - 3(x - y) - 2(x - y) + (x - y)2
= 3[2 - (x - y)] - (x - y)[2 - (x - y)]
= 3(2 - x + y) - (x - y)(2 - x + y)
= (2 - x + y)(3 - x + y)
Factorise the following:
Factorise the following:
p4 + 23p2q2 + 90q4
P4 + 23p2q2 + 90q4
= p4 + 18p2q2 + 5p2q2 + 90q4
= p2(p2 + 18q2) + 5q2(p2 + 18q2)
= (p2 + 18q2)(p2 + 5q2)
Factorise the following:
2a3 + 5a2b - 12ab2
2a3 + 5a2b - 12ab2
= 2a3 + 8a2b - 3a2b - 12ab2
= 2a2(a + 4b) - 3ab(a + 4b)
= (a + 4b)(2a2 - 3ab)
= (a + 4b)a(2a - 3b)
= a(a + 4b)(2a - 3b)
Chapter 5 - Factorisation Exercise Ex. 5.3
Factorise the following by the difference of two squares:
x2 - 16
x2 - 16
= x2 - 42
= (x - 4)(x + 4)
Factorise the following by the difference of two squares:
64x2 - 121y2
64x2 - 121y2
= (8x)2 - (11y)2
= (8x - 11y)(8x + 11y)
Factorise the following by the difference of two squares:
441 - 81y2
441 - 81y2
= (21)2 - (9y)2
= (21 - 9y)(21 + 9y)
= 3(7 - 3y)3(7 + 3y)
= 9(7 - 3y)(7 + 3y)
Factorise the following by the difference of two squares:
x6 - 196
x6 - 196
= (x3)2 - (14)2
= (x3 - 14)(x3 + 14)
Factorise the following by the difference of two squares:
625 - b2
625 - b2
= (25)2 - (b)2
= (25 - b)(25 + b)
Factorise the following by the difference of two squares:
Factorise the following by the difference of two squares:
8xy2 - 18x3
8xy2 - 18x3
= 2x(4y2 - 9x2)
= 2x[(2y)2 - (3x)2]
= 2x[(2y - 3x)(2y + 3x)]
= 2x(2y - 3x)(2y + 3x)
Factorise the following by the difference of two squares:
16a4 - 81b4
16a4 - 81b4
= (4a2)2 - (9b2)2
= (4a2 - 9b2)(4a2 + 9b2)
= [(2a)2 - (3b)2](4a2 + 9b2)
= [(2a - 3b)(2a + 3b)](4a2 + 9b2)
= (2a - 3b)(2a + 3b)(4a2 + 9b2)
Factorise the following by the difference of two squares:
a(a - 1) - b(b - 1)
a(a - 1) - b(b - 1)
= a2 - a - b2 + b
= a2 - b2 - a + b
= (a2 - b2) - (a - b)
= (a - b)(a + b) - (a - b)
= (a - b)(a + b - 1)
Factorise the following by the difference of two squares:
(x + y)2 -1
(x + y)2 - 1
= (x + y)2 - (1)2
= (x + y + 1)(x + y - 1)
Factorise the following by the difference of two squares:
x2 + y2 - z2 - 2xy
x2 + y2 - z2 - 2xy
= x2 + y2 - 2xy - z2
= (x2 + y2 - 2xy) - z2
= (x - y)2 - (z)2
= (x - y - z)(x - y + z)
Factorise the following by the difference of two squares:
(x - 2y)2 -z2
(x - 2y)2 - z2
= (x - 2y)2 - (z)2
= (x - 2y - z)(x - 2y + z)
Factorise the following:
9(a - b)2 - (a + b)2
9(a - b)2 - (a + b)2
= [3(a - b)]2 - (a + b)2
= [3(a - b) - (a + b)][3(a - b) + (a + b)]
= (3a - 3b - a - b)(3a - 3b + a + b)
= (2a - 4b)(4a - 2b)
= 2(a - 2b)2(2a - b)
= 4(a - 2b)(2a - b)
Factorise the following:
25(x - y)2 - 49(c - d)2
25(x - y)2 - 49(c - d)2
= [5(x - y)]2 - [7(c - d)]2
= [5(x - y) - 7(c - d)][5(x - y) + 7(c - d)]
= (5x - 5y - 7c + 7d)(5x - 5y + 7c - 7d)
Factorise the following:
(2a - b)2 -9(3c - d)2
(2a - b)2 - 9(3c - d)2
= (2a - b)2 - [3(3c - d)]2
= [(2a - b) - 3(3c - d)][(2a - b) + 3(3c - d)]
= (2a - b - 9c + 3d)(2a - b + 9c - 3d)
Factorise the following:
b2 - 2bc + c2 - a2
b2 - 2bc + c2 - a2
= (b2 - 2bc + c2) - a2
= (b - c)2 - (a)2
= (b - c - a)(b - c + a)
Factorise the following:
Factorise the following:
(x2 + y2 - z2)2 - 4x2y2
(x2 + y2 - z2)2 - 4x2y2
= (x2 + y2 - z2)2 - (2xy)2
= (x2 + y2 - z2 - 2xy)(x2 + y2 - z2 + 2xy)
= [(x2 + y2 - 2xy) - z2][(x2 + y2 + 2xy) - z2]
= [(x - y)2 - z2][(x + y)2 - z2]
= [(x - y - z)(x - y + z)][(x + y - z)(x + y + z)]
= (x - y - z)(x - y + z)(x + y - z)(x + y + z)
Factorise the following:
a2 + b2 - c2 - d2 + 2ab - 2cd
a2 + b2 - c2 - d2 + 2ab - 2cd
= (a2 + b2 + 2ab) - (c2 + d2 + 2cd)
= (a + b)2 - (c + d)2
= (a + b + c + d)(a + b - c - d)
Factorise the following:
4xy - x2 - 4y2 + z2
4xy - x2 - 4y2 + z2
= z2 - x2 - 4y2 + 4xy
= z2 - (x2 + 4y2 - 4xy)
= z2 - (x - 2y)2
= [z - (x - 2y)][z + (x - 2y)]
= (z - x + 2y)(z + x - 2y)
Factorise the following:
4x2 - 12ax - y2 - z2 - 2yz + 9a2
4x2 - 12ax - y2 - z2 - 2yz + 9a2
= (4x2 - 12ax + 9a2) - (y2 + z2 + 2yz)
= (2x - 3a)2 - (y + z)2
= [(2x - 3a) + (y + z)][(2x - 3a) - (y + z)]
= (2x - 3a + y + z)(2x - 3a - y - z)
Factorise the following:
(x + y)3 - x - y
(x + y)3 - x - y
= (x + y)(x + y)2 - (x + y)
= (x + y)[(x + y)2 - 1]
= (x + y)[(x + y + 1)(x + y - 1)]
= (x + y)(x + y + 1)(x + y - 1)
Factorise the following:
y4 + y2 + 1
y4 + y2 + 1
= y4 + 2y2 + 1 - y2
= (y2 + 1)2 - y2
= (y2 + 1 + y)(y2 + 1 - y)
Factorise the following:
(a2 - b2)(c2 - d2) - 4abcd
(a2 - b2)(c2 - d2) - 4abcd
= a2c2 - a2d2 - b2c2 + b2d2 - 4abcd
= a2c2 + b2d2 - 2abcd - a2d2 - b2c2 - 2abcd
= (a2c2 + b2d2 - 2abcd) - (a2d2 + b2c2 + 2abcd)
= (ac - bd)2 - (ad + bc)2
= [(ac - bd) + (ad + bc)][(ac - bd) - (ad + bc)]
= (ac - bd + ad + bc)(ac - bd - ad - bc)
Express each of the following as the difference of two squares:
(x2 - 2x + 3)(x2 + 2x + 3)
Express each of the following as the difference of two squares:
(x2 - 2x + 3) (x2 - 2x - 3)
Express each of the following as the difference of two squares:
(x2 + 2x - 3) (x2 - 2x + 3)
Factorise:
Factorise:
Factorise:
x4 + y4 - 6x2y2
Factorise:
4x4 + 25y4 + 19x2y2
Factorise:
Factorise:
5x2 - y2 - 4xy + 3x - 3y
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