Question

Expand : 

i. (a + 2)(a – 1) 

ii. (m – 4)(m + 6) 

iii. (p + 8) (p – 3) 

iv. (13 + x)(13 – x) 

v. (3x + 4y) (3x + 5y) 

vi. (9x – 5t) (9x + 3t)

vii. (m + (2/3)) (m - (7/3))

viii. (x + (1/x)) (x - (1/x))

ix. ((1/y) + 4) ((1/y) - 9)

Answer 1

i. (a + 2)(a – 1) 

= a² + (2 – 1) a + 2 × (-1) ... [∵ (x + A) (x + B) = x² + (A + B)x + AB] 

= a² + a – 2

ii. (m – 4)(m + 6) 

= m² + (- 4 + 6) m + (-4) × 6 …[∵ (x + a) (x + b) = x² + (a + b)x + ab] 

= m² + 2m – 24 

iii. (p + 8) (p – 3) 

= p² + (8 – 3) p + 8 x (-3) …[∵ (x + a) (x + b) = x² + (a + b)x + ab] 

= p² + 5p – 24 

iv. (13 + x) (13 – x) 

= (13)² + (x – x) 13 + x × (-x) …[∵ (x + a) (x + b) = x² + (a + b)x + ab] = 169 + 0 × 13 – x² 

= 169 – x² 

v. (3x + 4y) (3x + 5y) 

= (3x)² + (4y + 5y) 3x + 4y × 5y …[∵ (x + a) (x + b) = x² + (a + b)x + ab] 

= 9x² + 9y × 3x + 20y² = 9x² + 27xy + 20y²

vi. (9x – 5t) (9x + 3t) 

= (9x)² + [(-5t) + 3t] 9x + (-5t) × 3t …[∵ (x + a) (x + b) = x² + (a + b)x + ab] 

= 81x² + (-2t) × 9x – 15t² 

= 81x² – 18xt – 15t²

vii. (m + (2/3)) (m - (7/3))

viii. (x + (1/x)) (x - (1/x))

ix. ((1/y) + 4) ((1/y) - 9)