# How do you factor a perfect square trinomial  x^2-2x+1?

Jun 2, 2015

${x}^{2} - 2 x + 1 = {x}^{2} - 2 x + {1}^{2} = {\left(x - 1\right)}^{2}$

A perfect square trinomial is the square of a binomial, so will take the form:

${a}^{2} + 2 a b + {b}^{2}$

since ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

So a perfect square trinomial satisfies the following conditions:

(1) Two of the terms are squares.
(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.

If the two square terms are ${a}^{2}$ and ${b}^{2}$ then the trinomial is either ${\left(a + b\right)}^{2}$ or ${\left(a - b\right)}^{2}$ depending on the sign of the third term.