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
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)
Expand the following:
a. (a + 3b)2
b. (2p - 3q)2
c.
d. (x - 3y - 2z)2
Find the squares of the following:
a. 9m - 2n
b. 3p -4q2
c.
d. (2a + 3b - 4c)
Evaluate the following without multiplying:
a. (95)2
b. (103)2
c. (999)2
d. (1005)2
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
find: (i) x - y,
(ii) x2 - y2.
If p + q = 8 and p - q = 4, find:
(i) pq,
(ii) p2 + q2
If m - n = 0.9 and mn = 0.36, find:
a. m + n,
b. m2 - n2.
If x + y = 1 and xy = -12; find
(i) x - y,
(ii) x2 - y2.
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Chapter 4 - Expansions Exercise Ex. 4.2
(v)

If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
If x3 + y3 = 9 and x + y = 3, find xy.
If a + b = 5 and ab = 2, find a3 + b3.
If p - q = -1 and pq = -12, find p3 - q3
If m - n = -2 and m3 - n3 = -26, find mn.
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Simplify:
(4x + 5y)2 + (4x - 5y)2
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(a + b)3 + (a - b)3
Simplify:
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
Simplify:
(2x + y)(4x2 - 2xy + y2)
Simplify:
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Simplify:
(4m - 5n - 8)(4m - 5n + 5)
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