Question

what is a perfect square trinomial ​

Answer 1

An expression obtained from the square of binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac. The perfect square formula takes the following forms: (ax)2 + 2abx + b2 = (ax + b)

Answer 2

Your Question :

What is a perfect square trinomial?

Simple Answer :

A trinomial which can be expressed as the square of a binomial is called a perfect-square trinomial. Two examples of such trinomials are a² + 2ab + b² , i.e. (a + b)² , and a² - 2ab + b² , i.e. (a - b)².

Characteristics -

In a perfect-square trinomial,

i) two terms are perfect square

ii) the third term ( which may br positive or negative) is twice the product of the square roots of the other two terms.

Example -

Consider the expression 4a² + 4a + 1

Here, 4a² = (2a)² , 1 = 1² and 4a = 2 × 2a × 1 = (twice the product of the square roots of the other two terms).

Thus, this is a perfect square trinomial that can bs expressed as the square of a binomial as follows :

4a² + 4a + 1 = (2a)² + 2 × 2a × 1 + 1² = (2a + 1)²

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