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

User Etranz
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2 Answers

3 votes
(x-2)^2 is the answer.
User Amarjeet
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7 votes

Answer:

(x - 2)²

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

User Amey Dahale
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