How do you simplify #(sqrtx-sqrt7)(sqrtx+sqrt7)#?

2 Answers
Sep 5, 2016

Answer:

#x - 7#

Explanation:

We have: #(sqrt(x) - sqrt(7)) (sqrt(x) + sqrt(7))#

Let's expand the parentheses:

#= (sqrt(x)) (sqrt(x)) + (sqrt(x)) (sqrt(7)) + (- sqrt(7)) (sqrt(x)) + (- sqrt(7)) (sqrt(7))#

#= x + sqrt(7 x) - sqrt(7 x) - 7#

#= x - 7#

Sep 5, 2016

Answer:

#x-7#

Explanation:

Recall: difference of squares can be factored:

#x^2 - y^2 = (x+y)(x-y)#

The reverse is also true, if 2 brackets are the same with different signs, we find that:

#(m+n)(m-n) = m^2 -n^2#

This is what we have in this question,

#(sqrtx -sqrt7)(sqrtx + sqrt7) = (sqrtx)^2 - (sqrt7)^2#

=#x-7#