# 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.

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## 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.
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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