Perfect Square Trinomial Formula

An expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if 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 Example

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

Solution:

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

Alternatively,

x² – 6x + 9 = x² – 2(3)(x) + 3²

= (x – 3)²

The factors of the given equation are a perfect square.

So, the given trinomial is a perfect square.