# Multiplying polynomials by monomials

### Multiplying polynomials by monomials

This section will teach us how to multiply a polynomial (more than one term) by a monomial (one term only). We will use an area model as an aid to do the multiplication. We will then try to solve the questions without using the model. At the end, we will look at some of the related word problems.

#### Lessons

• 1.
Multiply each expression by using an area model.
a)
$\left( {3x} \right)\left( {7x + 4} \right)$

b)
$\left( {2x + 8} \right)\left( {1.6x} \right)$

• 2.
Multiply.
a)
$\left( {4.6} \right)\left( {3x - 8} \right)$

b)
$\left( {5x} \right)\left( {2x - 1.2} \right)$

c)
$\left( {4x - 1} \right)\left( {6x} \right)$

d)
$\left( {13 - 9x} \right)\left( {2.3x} \right)$

e)
$\left( {3x} \right)\left( {2x + 5y + 7} \right)$

f)
$\left( {\frac{1}{4}x - 2} \right)\left( { - x} \right)$

• 3.
The width of a rectangular grass field is 1.5 m shorter than 0.7 times the length.
a)
Determine the expression for the area of the field.

b)
If the width is 6.9 m, what is the area of the field?