Question

What is the value of k?

Answer 1

`( {x}^(2) + 16x + 64) - (x + 8)(x - 4) = k(x + 8) \\ ( {x + 8)}^(2) - (x + 8)(x - 4) = k(x + 8) \\ (x + 8) - (x - 4) = k \\ k = (x - x) + (8 + 4) \\ k = 12`

Answer 2

Explanation:

a² + 2ab + b² = (a + b)²

2ab = 2 * x * 8 = 16x

x² + 16x + 64 = x² + 2* x * 8 + 8²

= (x + 8)²

x² + 16x + 8 - (x +8)(x - 4) = (x+8)² - (x+ 8) (x -4)

= (x +8)(x +8) - (x + 8)(x - 4)

(x +8 ) is common in both terms

= (x + 8) [ (x + 8) - (x - 4) ]

= (x + 8) [ x + 8 - x + 4 ]

{Combine like terms. so x + (-x ) = 0 and 8 +4 = 12}

= (x + 8) [ 12]

k = 12