How do you multiply (4x+2y+2) (4x+2y-2)?

Jun 27, 2018

$\left(4 x + 2 y + 2\right) \left(4 x + 2 y - 2\right) = 16 {x}^{2} + 16 x y + 4 {y}^{2} - 4$

Explanation:

We can write $\left(4 x + 2 y + 2\right) \left(4 x + 2 y - 2\right)$ as $\left(z + 2\right) \left(z - 2\right)$,

where $z = 4 x + 2 y$ and

$\left(4 x + 2 y + 2\right) \left(4 x + 2 y - 2\right) = \left(z + 2\right) \left(z - 2\right)$

= ${z}^{2} - 4$

= ${\left(4 x + 2 y\right)}^{2} - 4$

= ${\left(4 x\right)}^{2} + 2 \cdot 4 x \cdot 2 y + {\left(2 y\right)}^{2} - 4$

= $16 {x}^{2} + 16 x y + 4 {y}^{2} - 4$