Factor perfect squares and differences of squares. Factor. x^2-4x+4

(x - 2) ²

Step-by-step explanation:

We know an equation in standard form ax²+bx+c is a perfect square if:

± [2*√ (ax²) * √ (c) ] = bx

Test for : x²-4x+4

± [2*√ (ax²) * √ (c) ] = bx

± [2*√ (x²) * √ (4) ] = - 4x

± [2*x*2] = - 4x

-4x = - 4x

Therefore this trinomial is a perfect square.

To factor:

(√ (ax²) ± √ (c)) ²

± depends on if the sign before the "b" value is positive or negative.

In x²-4x+4, it's negative.

x²-4x+4

= (√ (ax²) ± √ (c)) ²

= (x - 2) ²

(x-2) ^2 is the answer.