### Question

**The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to**

A. 0

B. 0.28

C. 0.26

D. 1

#### Answer: B. 0.28

**Solution:**

(a+b)^{2} = a^{2}+2ab+b^{2}

12.86 × 12.86 + 12.86 × p + 0.14 × 0.14

= (12.86)^{2} + 12.86 × p + (0.14)^{2}

This can be written as (12.86 + 0.14)^{2} = 132,

if 12.86 × p = 2 × 12.86 × 0.14

i.e., if p = 2 × 0.14 = 0.28

Hence, **p = 0.28** is the answer