## 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

Solution 6
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
Solution 16
Question 17
If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.
Solution 17
Question 18
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
Solution 18
Question 19
If x3 + y3 = 9 and x + y = 3, find xy.
Solution 19
Question 20
If a + b = 5 and ab = 2, find a3 + b3.
Solution 20
Question 21
If p - q = -1 and pq = -12, find p3 - q3
Solution 21
Question 22
If m - n = -2 and m3 - n3 = -26, find mn.
Solution 22
Question 23
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
Solution 23
Question 24
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Solution 24
Question 25
Simplify:
(4x + 5y)2 + (4x - 5y)2
Solution 25
Question 26
Simplify:
(7a +5b)2 - (7a - 5b)2
Solution 26
Question 27
Simplify:
(a + b)3 + (a - b)3
Solution 27
Question 28
Simplify:

Solution 28
Question 29
Simplify:
(x + y - z)2 + (x - y + z)2
Solution 29
Question 30
Simplify:

Solution 30
Question 31
Simplify:
(2x + y)(4x2 - 2xy + y2)
Solution 31
Question 32
Simplify:

Solution 32
Question 33
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Solution 33
Question 34
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Solution 34
Question 35
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Solution 35
Question 36
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Solution 36
Question 37
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Solution 37
Question 38
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Solution 38
Question 39
Simplify:
(4m - 5n - 8)(4m - 5n + 5)
Solution 39
Question 40
Solution 40