# How do you simplify (3sqrta -7)(3sqrta +7)?

Aug 17, 2017

This can be simplified to $9 a - 49$. See explanation.

#### Explanation:

If we have a product of 2 expressions with different signs we can write it as the difference of squares of the expressions.

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

Here the squares are:

and

## ${7}^{2} = 49$

Aug 17, 2017

color(magenta)(9a-49

#### Explanation:

$\left(3 \sqrt{a} - 7\right) \left(3 \sqrt{a} + 7\right)$

$\therefore \textcolor{w h i t e}{a a a a a}$color(magenta)(sqrtaxxsqrta=a

$\therefore \textcolor{w h i t e}{a a a}$$3 \sqrt{a} \times 3 \sqrt{a} = 9 a$------------(1)

$\therefore \textcolor{w h i t e}{a}$$\textcolor{w h i t e}{a a a}$$- 7 \times + 7 = - 49$--------(2)

$\therefore \textcolor{w h i t e}{a a a a}$$- 7 \times 3 \sqrt{a} = - 21 \sqrt{a}$----(3)

$\therefore \textcolor{w h i t e}{a a a a a a}$$7 \times 3 \sqrt{a} = 21 \sqrt{a}$--------(4)

color(magenta)((1)+(2)+(3)+(4)

$\therefore 9 a - 49 - 21 \sqrt{a} + 21 \sqrt{a}$

:.color(magenta)(=9a-49