Question

Which of the following expressions is equivalent to the expression 706 × 695?

• A. (600)² + 600 − 6 × 5
• B. (700)² + 700 − 6 × 5
• C. 600² + (95 + 6) 600 − 11
• D. 700² + (95 + 6) 700 − 11

Answer 1

The correct option is B

(700)² + 700 − 6 × 5

We can write 706 × 695 as (700 + 6)(700 − 5).

This expression is of the form (x + a) (x + b), where x = 700, a = 6, and b = − 5.

∴ 706 × 695 = (700 + 6) (700 − 5)

= (700)² + (6 − 5) × 700 + 6 × (− 5)

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

⇒ 706 × 695 = (700)² + 700 − 6 × 5