Question

Which equation is true?

9x2 - 25 = (3x - 5)(3x - 5)
9x2 - 25 = (3x - 5)(3x + 5)
9x2 – 25 = -(3x + 5)(3x + 5)
9x2 - 25 = -(3x + 5)(3x - 5) ​

Answer 1

`(3x-5)(3x+5)`

Explanation:

Difference of squares states that:

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

In this case...

`a^2=9x^2\\√(a^2)=√(9x^2)\ (take\ the\ square\ root\ of\ both\ sides)\\a=3x`

`b^2=25\\√(b^2)=√(25)\ (take\ the\ square\ root\ of\ both\ sides)\\b=5`

This means that...

`9x^2-25=(3x-5)(3x+5)`