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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