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Perfect Square Trinomial Formula

An expression obtained from the square of binomial equation is a perfect square trinomial. If a trinomial is in the form ax2 + bx + c is said to be perfect square, if only it satisfies the condition b2 = 4ac.

The Perfect Square Trinomial Formula is given as,

\[\large (ax)^{2}+2abx+b^{2}=(ax+b)^{2}\]

\[\large (ax)^{2}-2abx+b^{2}=(ax-b)^{2}\]

Solved Examples

Question: Is the trinomial x2 – 6x + 9 a perfect square?


x2 – 6x + 9
= x2 – 3x – 3x + 9
= x(x – 3) – 3(x – 3)
= (x – 3)(x – 3)

The factors of the given equation are a perfect square.

So, the trinomial is a perfect square.

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