Q. 230 - Intermediate Algebra

Question

How do you recognize the binomial squares pattern?

Step-by-Step Solution

Answer

We can recognize the pattern by squaring a binomial and the product is a perfect square trinomial.

Step 1. Given Information

The given pattern is binomial square pattern

Step 2. Explanation

As we know the trinomial $a{x}^2+bx+c$ is called a perfect square trinomial, if it is the square of binomial $(ax+b)$.

Now, to make use of binomial square pattern, recognize that a given trinomial fits it.

First check if the leading coefficient is a perfect square. Next we will check that the last term is a perfect square and then check the middle term is it twice the product of both the terms.

If everything checks easily, write the factors.

When middle term is negative, use the pattern $a^2-2ab+b^2={(a-b)}^2$

And when middle term is positive, use the pattern $a^2+2ab+b^2={(a+b)}^2$