(i) 4p² – 9q²
Answer: This can be factorised by using the equation; (a + b)(a – b) = a2 – b2
Factors = (2p + 3q)(2p – 3q)
(ii) 63a² – 112b²
Answer: 63a2 – 112b2 = 7(9a2 – 16b2)
= 7(3a + 4b)(3a – 4b)
(iii) 49x² – 36
Answer: (7x + 6)(7x – 6)
(iv) 16x5 – 144x³
Answer:16x5-144x3
= x³(16x²-144)
= x³(4x+12)(4x-12)
(v) (l + m) ² – (l – m) ²
Answer: (l + m + l – m)(l + m – l + m)
2l x 2m = 4lm
(vi) 9x² y² – 16
Answer: (3xy + 4)(3x – 4)
(vii) (x² – 2xy + y²) – z²
Answer: (x2 – 2xy + y2) – z2
= (x – y)2 – z2
= (x – y + z)(x – y – z)
(viii) 25a² – 4b² + 28bc – 49c²
Answer: 25a2 – 4b2 + 28bc – 49c2
= (5a)2 – (2b)2 + 2 x 2b x 7c – (7c)2
= (5a)2 – [(2b)2 – 2 x 2b x 7c + (7c)2]
= (5a)2 – (2b – 7c)2
This can be further factorised by using (a + b)(a – b) = a2 – b2
= (5a + 2b – 7c)(5a – 2b + 7c)
