Perfect Square Trinomial Formula
The perfect square trinomial formula helps in solving the complex trinomial function. A perfect square trinomial function is the one that is obtained by squaring the binomial expression. A trinomial will be a perfect square if and only if it is in the form ax^{2} + bx + c and satisfies the condition b^{2} = 4ac. Let us understand the perfect square trinomial formula using solved examples.
What is Perfect Square Trinomial Formula?
When a binomial expression is squared, we get the trinomial which is a perfect square of the binomial. The perfect square trinomial formula can take two different forms. The forms that the perfect square trinomial formula represents are:
\((ax)^2 + 2abx + b^2 = (ax + b)^2\)
\((ax)^2  2abx + b^2 = (ax  b)^2\)
Let us understand the perfect square trinomial formula better using a few solved examples.
Solved Examples Using Perfect Square Trinomial Formula

Example 1: Find the factors of x^{2} + 6x + 9 using the perfect square trinomial formula.
Solution:
Writing the given expression as (ax)^{2} + 2abx + b^{2},
x^{2} + 6x + 9 = (1)x^{2} + 2(1)(3)x + 3^{2}Using the perfect square trinomial formula,
\((ax)^2 + 2abx + b^2 = (ax + b)^2\)
We get,
x^{2} + 6x + 9 = (x + 3)^{2}Answer: Hence the factor of x^{2} + 6x + 9 is x + 3.

Example 2: Find the factors of x^{2} + 8x + 16 using the perfect square trinomial formula.
Solution:
Writing the given expression as (ax)^{2} + 2abx + b^{2},
x^{2} + 8x + 16 = (1)x^{2} + 2(1)(4)x + 4^{2}Using the perfect square trinomial formula,
\((ax)^2 + 2abx + b^2 = (ax + b)^2\)
We get,
x^{2} + 8x + 16 = (x + 4)^{2}Answer: Hence the factor of x^{2} + 8x + 16 is x + 4.
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