# How do you find the product of (-6x-7y^2)^2?

Apr 11, 2018

The final product is $36 {x}^{2} + 84 x {y}^{2} + 49 {y}^{4}$.

#### Explanation:

First, you can factor out a negative one:

$\textcolor{w h i t e}{=} {\left(- 6 x - 7 {y}^{2}\right)}^{2}$

$= {\left(- 1 \cdot \left(6 x + 7 {y}^{2}\right)\right)}^{2}$

$= {\left(- 1\right)}^{2} \cdot {\left(6 x + 7 {y}^{2}\right)}^{2}$

$= 1 \cdot {\left(6 x + 7 {y}^{2}\right)}^{2}$

$= {\left(6 x + 7 {y}^{2}\right)}^{2}$

Then, write out the actual multiplication:

$= \left(6 x + 7 {y}^{2}\right) \left(6 x + 7 {y}^{2}\right)$

Now, multiply each combination of the factors (called FOIL method):

$= 6 x \cdot 6 x + 6 x \cdot 7 {y}^{2} + 7 {y}^{2} \cdot 6 x + 7 {y}^{2} \cdot 7 {y}^{2}$

$= 36 {x}^{2} + 42 x {y}^{2} + 42 x {y}^{2} + 49 {y}^{4}$

$= 36 {x}^{2} + 84 x {y}^{2} + 49 {y}^{4}$

That's the product. Hope this helped!

Apr 11, 2018

(-6x-7y^2)^2=color(blue)(36x^2+84xy^2+49y^4

#### Explanation:

Given:

${\left(- 6 x - 7 {y}^{2}\right)}^{2}$

Use the square of a difference:

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$,

where:

$a = - 6 x$, and $b = 7 {y}^{2}$.

${\left(- 6 x - 7 {y}^{2}\right)}^{2} =$

${\left(- 6 x\right)}^{2} - 2 \left(- 6 x\right) \left(7 {y}^{2}\right) + {\left(7 {y}^{2}\right)}^{2}$

Simplify.

$36 {x}^{2} + 84 x {y}^{2} + 49 {y}^{4}$