Answer:
(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
