# How do you multiply (5y-2)(5y+2)?

Aug 18, 2016

25y^2-4#.

#### Explanation:

Using the Identity $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$.

$\therefore \left(5 y - 2\right) \left(5 y + 2\right) = {\left(5 y\right)}^{2} - {2}^{2} = 25 {y}^{2} - 4$.

Aug 18, 2016

$25 {y}^{2} - 4$

#### Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket. This can be achieved as follows.

$\left(\textcolor{red}{5 y - 2}\right) \left(5 y + 2\right) = \textcolor{red}{5 y} \left(5 y + 2\right) \textcolor{red}{- 2} \left(5 y + 2\right)$

now distribute each pair of brackets and collect 'like terms'

$= 25 {y}^{2} + \cancel{10 y} - \cancel{10 y} - 4 = 25 {y}^{2} - 4$