Mathematics » Introducing Polynomials » Using Multiplication Properties of Exponents

Multiplying Monomials

Multiplying Monomials

Since a monomial is an algebraic expression, we can use the properties for simplifying expressions with exponents to multiply the monomials.

Example

Multiply: \(\left(4{x}^{2}\right)\left(-5{x}^{3}\right).\)

Solution

 \(\left(4{x}^{2}\right)\left(-5{x}^{3}\right)\)
Use the Commutative Property to rearrange the factors.\(4·\left(-5\right)·{x}^{2}·{x}^{3}\)
Multiply.\(-20{x}^{5}\)

Example

Multiply: \(\left(\frac{3}{4}\phantom{\rule{0.1em}{0ex}}{c}^{3}d\right)\left(12c{d}^{2}\right).\)

Solution

 \(\left(\frac{3}{4}\phantom{\rule{0.1em}{0ex}}{c}^{3}d\right)\left(12c{d}^{2}\right)\)
Use the Commutative Property to rearrange the factors.\(\frac{3}{4}·12·{c}^{3}·c·d·{d}^{2}\)
Multiply.\(9{c}^{4}{d}^{3}\)

Optional Video: Multiply Monomials

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