Question

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

Answer 1

This can be simplified to `9a-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.

`(a-b)xx(a+b)=a^2-b^2`

Here the squares are:

`(3sqrt(a))^2=9a`

and

`7^2=49`

Answer 2

`color(magenta)(9a-49`

Explanation:

`(3sqrta-7)(3sqrta+7)`

`:.color(white)(aaaaa)` `color(magenta)(sqrtaxxsqrta=a`

`:.color(white)(aaa)` `3sqrtaxx3sqrta=9a`------------(1)

`:.color(white)(a)` `color(white)(aaa)` `-7xx+7=-49`--------(2)

`:.color(white)(aaaa)` `-7xx3sqrta=-21sqrta`----(3)

`:.color(white)(aaaaaa)` `7xx3sqrta=21sqrta`--------(4)

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

`:.9a-49-21sqrta+21sqrta`

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