# What is the missing term in the factorization?

May 20, 2018

4

#### Explanation:

$\text{ } 18 {x}^{2} - 32$

$= 2 \left(9 {x}^{2} - 16\right)$ --- notice this is a difference of perfect squares.

difference of perfect squares rule: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$= 2 \left(9 {x}^{2} - 16\right)$

=2(3x+4)(3x-4))

so the missing term is $4$

May 20, 2018

The missing value is $y = 4$, see explanations below.

#### Explanation:

18x²-32=2(3x+y)(3x-4)
2(9x²-16)=2(3x+4)(3x-4)
2((3x)²-4²)=2(3x+4)(3x-4)
Because a²-b²=(a+b)(a-b),
$2 \left(3 x + 4\right) \left(3 x - 4\right) = 2 \left(3 x + y\right) \left(3 x - 4\right)$
By identification, we can clearly see that the missing value is $y = 4$