# How do you find the product of (-y-3x)(-y+3x)?

Feb 26, 2017

See the entire solution process below:

#### Explanation:

Solution 1) We can use this formula:

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

Substituting $- y$ for $a$ and $3 x$ for $b$ gives:

$\left(- y + 3 x\right) \left(- y - 3 x\right) = {\left(- y\right)}^{2} - {\left(3 x\right)}^{2} = {y}^{2} - 9 {x}^{2}$

Solution 2) To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{- y} - \textcolor{red}{3 x}\right) \left(\textcolor{b l u e}{- y} + \textcolor{b l u e}{3 x}\right)$ becomes:

$\left(\textcolor{red}{- y} \times \textcolor{b l u e}{- y}\right) + \left(\textcolor{red}{- y} \times \textcolor{b l u e}{3 x}\right) - \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{- y}\right) - \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{3 x}\right)$

${\left(- y\right)}^{2} - 3 x y + 3 x y - 9 {x}^{2}$

We can now combine like terms:

${y}^{2} + \left(- 3 + 3\right) x y - 9 {x}^{2}$

${y}^{2} + 0 x y - 9 {x}^{2}$

${y}^{2} - 9 {x}^{2}$