Chapter 14.5, Problem 40HP

To determine

To compare: Procedure for multiply two binomial and for multiply binomial with monomial.

Answer to Problem 40HP

When we multiply binomial with binomial we three terms and we multiply binomial with monomial we have two terms.

Explanation of Solution

Given information:

To multiply two binomials and multiply binomials with monomial.

Formula:

  $\left(ax+b\right)\left(cx+d\right)=\left(ac{x}^2+\left(ad+bc\right)x+bd\right)$

  $\left(ax+b\right)x=a{x}^2+bx$ .

Calculation:

Consider the statement to multiply two binomials and multiply binomials with monomial.

When we multiply the binomial with binomial.

Recall that $\left(ax+b\right)\left(cx+d\right)=\left(ac{x}^2+\left(ad+bc\right)x+bd\right)$

Therefore we will have three terms.

When we multiply the binomial with monomial.

Recall that $\left(ax+b\right)x=a{x}^2+bx$ .

Therefore we have only two terms.