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. $$9{c}^{4}{d}^{3}$$