How do you factor the expression #9x^2 - 30x +25#?

1 Answer
George C.
Dec 28, 2015

#9x^2-30x+25 = (3x-5)^2#

Explanation:

This is a perfect square trinomial.

In general #(a+-b)^2 = a^2+-2ab+b^2#

Notice that both #9x^2 = (3x)^2# and #25 = 5^2# are perfect squares, so the only question is whether the middle term matches when you square #(3x-5)#, the minus sign being chosen to at result in a negative coefficient for the middle term.

#(3x-5)^2 = (3x)^2-2(3x)(5)+5^2 = 9x^2-30x+25#

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