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 + \(\frac{2}{3}\)) (m - \(\frac{7}{3}\))

viii. (x + \(\frac{1}{x}\)) (x - \(\frac{1}{x}\))

ix. (\(\frac{1}{y} +4\)) \((\frac{1}{y} - 9)\)

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 + \(\frac{2}{3}\)) (m - \(\frac{7}{3}\))

viii. (x + \(\frac{1}{x}\)) (x - \(\frac{1}{x}\))

 ix. (\(\frac{1}{y} +4\)) \((\frac{1}{y} - 9)\)