### Home > CCG > Chapter 2 > Lesson 2.2.2 > Problem2-74

2-74.

Review how to multiply binomials by reading the Math Notes box for this lesson. Then rewrite each of the expressions below by multiplying binomials and simplifying the resulting expression.

Review the method for multiplying binomials.

1. $(4x+1)(2x-7)$

Draw a rectangle with its width and length each divided once.

Label the rectangle's length with the first binomial, with one term corresponding to each half.

 top edge left $4x$ top edge right $+1$ left edge top $-7$ interior top left empty interior top right empty left edge bottom$2x$ interior bottom left empty interior bottom right empty

Do the same for the width and the second binomial.

For each of the four portions of the rectangle, find the product of the term on its width and the term on its length.

 top edge left $4x$ top edge right $+1$ left edge top $-7$ interior top left $-28x$ interior top right $-7$ left edge bottom$2x$ interior bottom left$8x^2$ interior bottom right $2x$

$8x^2-26x-7$

Follow the same steps for parts (b) through (d).

1. $(5x-2)(2x+7)$

1. $(4x-3)(x-11)$

1. $(-3x+1)(2x-5)$