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

2 Answers
Daniel L.
Aug 17, 2017

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

Barney V.
Aug 17, 2017

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

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