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Theory

Factor the perfect square trinomial

An expression of the form

a^{2} - 2 a b + b^{2}

can be factored to a perfect square.

a^{2} - 2 a b + b^{2} = (a - b)^{2}

An example is the expression

x^{2} - 10 x + 25

which can be written as

x^{2} - 2 \cdot x \cdot 5 + 5^{2},

and thus, be factored to the square of the binomial

x - 5 .

x^{2} - 2 \cdot x \cdot 5 + 5^{2} = (x - 5)^{2}

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