Question

What is the value of k?

Answer 1

Answer:

Step-by-step 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

Answer 2

Answer:

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