Evaluate the following(i) (2x – 3) (2x + 5)(ii) (y – 7) (y + 3)(ii

1.	Evaluate the following(i) (2x – 3) (2x + 5)(ii) (y – 7) (y + 3)(iii) 107 × 103
Answer» (i) (2x – 3) (2x + 5) = (2x)² + (-3 + 5) (2x) + (-3) (5) [∵ (x + a) (x + b) = x² + (a + b)x + ab] = 2²x² + 2 × 2x + (-15) = 4x² + 4x – 15 (ii) (y – 7) (y + 3) = y² + (-7 + 3)y + (-7) (3) [∵ (x + a)(x + b) = x² + (a + b)x + ab] = y² – 4y + (-21) = y² – 4y – 21 (iii) 107 × 103 = (100 + 7) × (100+ 3) = 100² + (7 + 3) × 100 +(7 × 3) = 10000 + 10 × 100 + 21 = 10000 + 1000 + 21 = 11021

Evaluate the following(i) (2x – 3) (2x + 5)(ii) (y – 7) (y + 3)(iii) 107 × 103

Answer»

(i) (2x – 3) (2x + 5)

= (2x)² + (-3 + 5) (2x) + (-3) (5)

[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= 2²x² + 2 × 2x + (-15)

= 4x² + 4x – 15

(ii) (y – 7) (y + 3)

= y² + (-7 + 3)y + (-7) (3)

[∵ (x + a)(x + b) = x² + (a + b)x + ab]

= y² – 4y + (-21)

= y² – 4y – 21

(iii) 107 × 103

= (100 + 7) × (100+ 3)

= 100² + (7 + 3) × 100 +(7 × 3)

= 10000 + 10 × 100 + 21

= 10000 + 1000 + 21

= 11021