Chapter 8.7, Problem 52P

Reasoning Explain how reversing the rules for multiplying squares of binomials can help you factor a perfect-square trinomial.

To determine

how reversing the rules of multiplying squares of binomials would be useful to factor a perfect square trinomial

Answer to Problem 52P

Reversing the rules of multiplying squares of binomials would be useful to factor a perfect square trinomial

Explanation of Solution

Given information:

Condition of factorising a perfect square trinomial

Calculation:

Consider squaring a binomial as follows:

  ${\left(a+b\right)}^2=a^2+2ab+b^2$

Or

  ${\left(a-b\right)}^2=a^2-2ab+b^2$

It would be useful to reverse the rule since it is much easier to check for the first and last terms for perfect squares and middle term to be the twice product of one of the terms from first and last terms of the expression in order to factor a perfect trinomial