How do you factor #25x^2-9#?

1 Answer
Stefan V.
Jul 26, 2015

You write the expression as a difference of two perfect squares.

Explanation:

You can factor your expression by writing it as a difference of two perfect squares, for which you know that

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

In your case, you can write

#25x^2 - 9 = 5x * 5x - 3 * 3#, which is equivalent to

#(5x)^2 - 3^2 = color(green)((5x-3)(5x+3))#

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