How to multiply a monomial by a polynomial

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PSAT Math › How to multiply a monomial by a polynomial

Questions 1 - 4

1

If you have a rectangle with a width of and a length of , what is the area of the rectangle?

$21n^{2}-9ny+6n$

$56n^{2}-27ny+18n$

$21n-9y^{2}+6$

$14ny^{3}$

Explanation

To find the area of a rectangle, multiply the length times the width. Therefore, you must multiply times . To do that, you must multiply the monomial times each part of the trinomial, like so:

2

Find the product:

Explanation

Use the distributive property:

Simplify: don't forget to use the rules of multiplying exponents (add them)

3

Find the product:

Explanation

Find the product:

Use the distributive property:

$(4a^2\cdot ab^2)+(4a^2\cdot a^2b)+(4a^2\cdot ac^3)$

When multiplying variables with exponents, add the exponents:

4

Find the product:

Explanation

Find the product:

Use the distributive property:

$(5x^3 \cdot x^2)+(5x^3 \cdot 2x)+(5x^3 \cdot 4)$

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