FRANK Solutions for Class 9 Maths Chapter 4 - Expansions
Learn to expand the given mathematical expressions with Frank Solutions for ICSE Class 9 Mathematics Chapter 4 Expansions. Practise the solutions to evaluate expressions without using the multiplication method. Also, revise the steps to find the cube of the given expression with the help of our chapter solutions.
Also, practise the Frank textbook solutions to relearn the methods for solving expansions-based problems. You can also solve related problems by accessing TopperLearning’s online sample question papers and previous years’ papers with solutions. And if you have trouble with difficult questions, get a response to your doubts on our ‘UnDoubt’ section.
Chapter 4 - Expansions Exercise Ex. 4.1
Question 1
Expand the following:
(i) (a + 4) (a + 7)
(ii) (m + 8) (m - 7)
(iii) (x - 5) (x - 4)
(iv) (3x + 4) (2x - 1)
(v) (2x - 5) (2x + 5) (2x- 3)
Solution 1
(V)
Question 2
Expand the following:
a. (a + 3b)2
b. (2p - 3q)2
c. 
d. (x - 3y - 2z)2
Solution 2
Question 3
Find the squares of the following:
a. 9m - 2n
b. 3p -4q2
c. 
d. (2a + 3b - 4c)
Solution 3
Question 4
Solution 4
Question 5
Evaluate the following without multiplying:
a. (95)2
b. (103)2
c. (999)2
d. (1005)2
Solution 5
Question 6
Evaluate, using (a + b)(a - b)= a2 - b2.
a. 399 x 401
b. 999 x 1001
c. 409 x 5.1
d. 15.9 x 16.1
Solution 6
Question 7
If a - b = 10 and ab = 11; find a + b.
Solution 7
Question 8
If x + y = 9, xy = 20;
find: (i) x - y,
(ii) x2 - y2.
find: (i) x - y,
(ii) x2 - y2.
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
If p + q = 8 and p - q = 4, find:
(i) pq,
(ii) p2 + q2
Solution 12
Question 13
If m - n = 0.9 and mn = 0.36, find:
a. m + n,
b. m2 - n2.
Solution 13
Question 14
If x + y = 1 and xy = -12; find
(i) x - y,
(ii) x2 - y2.
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Solution 17
Question 18
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Solution 18
Question 19
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
Solution 19
Question 20
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Solution 20
Question 21
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Solution 21
Chapter 4 - Expansions Exercise Ex. 4.2
Question 1
(v) 
Solution 1
(v)
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6(a)
Solution 6(a)
Question 6(b)
Solution 6(b)
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.
Solution 16
Question 17
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
Solution 17
Question 18
If x3 + y3 = 9 and x + y = 3, find xy.
Solution 18
Question 19
If a + b = 5 and ab = 2, find a3 + b3.
Solution 19
Question 20
If p - q = -1 and pq = -12, find p3 - q3
Solution 20
Question 21
If m - n = -2 and m3 - n3 = -26, find mn.
Solution 21
Question 22
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
Solution 22
Question 23
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Solution 23
Question 24(a)
Simplify:
(4x + 5y)2 + (4x - 5y)2
Solution 24(a)
Question 24(b)
Simplify:
(7a +5b)2 - (7a - 5b)2
Solution 24(b)
Question 24(c)
Simplify:
(a + b)3 + (a - b)3
Solution 24(c)
Question 24(d)
Simplify:
Solution 24(d)
Question 24(e)
Simplify:
(x + y - z)2 + (x - y + z)2
Solution 24(e)
Question 24(f)
Simplify:
Solution 24(f)
Question 24(g)
Simplify:
(2x + y)(4x2 - 2xy + y2)
Solution 24(g)
Question 24(h)
Simplify:
Solution 24(h)
Question 24(i)
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Solution 24(i)
Question 24(j)
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Solution 24(j)
Question 24(k)
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Solution 24(k)
Question 24(l)
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Solution 24(l)
Question 24(m)
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Solution 24(m)
Question 24(n)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Solution 24(n)
Question 24(o)
Simplify:
(4m - 5n - 8)(4m - 5n + 5)
Solution 24(o)
Question 25
Solution 25
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