# Factorisation

## Exercise 14.3 (Part)

(e) 5pq(p^2 – q^2) ÷ 2p (p + q)

Answer: 5pq(p^2 – q^2) ÷ 2p (p + q)
Using (a +b) (a – b) = a^2 – b^2; the equation can be written as follows:
= 5pq (p + q) (p – q) ÷ 2p (p + q)
= 5q(p – q) ÷ 2

(f) 12xy (9x^2 – 16y^2) ÷ 4xy (3x + 4y)

Answer: 12xy (9x^2 – 16y^2) ÷ 4xy (3x + 4y)
This can be solved as previous question;
= 3 (3x + 4y) (3x – 4y) ÷ (3x + 4y)
= 3 (3x – 4y)

(g) 39y^3(50y^2 – 98) ÷ 26y^2 (5y + 7)

Answer: 39y^3(50y^2 – 98) ÷ 26y^2 (5y + 7)
= 2 xx 39y^3(25y^2 – 49) ÷ 26y^2 (5y + 7)
= 3y (25y^2 – 49) ÷ (5y + 7)
= 3y (5y + 7) (5y – 7) ÷ (5y + 7)
= 3y (5y – 7)

## Exercise 14.4

Find and correct the errors in the following mathematical statements:

Question 1: 4(x – 5) = 4x – 5

Answer: 4(x – 5) = 4x – 20

Question 2: x(3x + 2) = 3x^2 + 2

Answer: = 3x^2 + 2x

Question 3: 2x + 3y = 5xy

Here; x and y are as different as chalk and cheese and hence cannot be added together.

Question 4: x + 2x + 3x = 5x

It is like adding one apple, two apples and three apples.

Question 5: 5y + 2y + y – 7y = 0

Answer: = y

Question 6: 3x + 2x = 5x^2

Answer: = 5x

Question 7: (2x)^2 + 4(2x) + 7 = 2x^2 + 8x + 7

Answer: = 4x^2 + 8x + 7

Question 8: (2x)^2 + 5x = 4x + 5x = 9x

Answer: 4x^2 + 5x

Question 9: (3x + 2)^2 = 3x^2 + 6x + 4

Answer: Using (a + b)^2 = a^2 + 2ab + b^2;
= 9x^2 + 12x + 4

Question 10: Substituting x = - 3 in

(a) x^2 + 5x + 4 gives (-3)^2 + 5 ( - 3) + 4 = 9 + 2 + 4 = 15

Answer: = (-3)^2 + 5( - 3) + 4
= 9 – 15 + 4 = - 2

(b) x^2 – 5x + 4 gives (-3)^2 – 5 (- 3) + 4 = 9 – 15 + 4 = - 2

Answer: (- 3)^2 – 5 ( - 3) + 4
= 9 + 15 + 4 = 28

(c) x^2 + 5x gives (-3)^2 + 6( -3) = - 9 – 15 = - 24

Answer: ( - 3)^2 + 5 ( - 3)
= 9 – 15 = - 6

Question 11: (y – 3)^2 = y^2 – 9

Answer: = y^2 – 6y + 9

Question 12: (z + 5)^2 = z^2 + 25

Answer: = z^2 + 10z + 25

Question 13: (2a + 3b) ( a – b) = 2a^2 – 3b^2

Answer: = 2a^2 – 2ab + 3ab – 3b^2
= 2a^2 + ab – 3b^2

Question 14: (a + 4)(a + 2) = a^2 + 8

Answer: = a^2 + 2a + 4a + 8 = a^2 + 6a + 8

Question 15: (a – 4)(a – 2) = a^2 – 8

Answer: a^2 – 2a – 4a + 8
= a^2 – 6a + 8

Question 16: 3x^2 ÷ 3x^2 = 0

Question 17: (3x^2 + 1) ÷ 3x^2 = 1 + 1 = 2

Answer: = 1 + (1)/(3x^2)

Question 18: 3x ÷ (3x + 2) = ½

Answer: = 3x ÷ (3x + 2)

Question 19: 3 ÷ (4x + 3) = 1/4x

Answer: = 3 ÷ (4x + 3)

Question 20: (4x + 5) ÷4x = 5

Answer: = 1 + (5)/(4x)

Question 21: (7x + 5) ÷ 5 = 7x

Answer: = (7x)/(5) + 1