Michigan Algebra II KHauck

We begin this section by multiplying a monomial by a monomial. As you saw in the introduction, when working with monomials multiply the coefficients separately and then apply the exponent rules to each variable. Let’s try some examples.

Step 1. Group coefficients and like bases.

3 ^. -6 ^. x ^. x^{4 .} y^{5 .} y²

Step 2. Multiply coefficients & apply the product rule of exponents.

(3 ^. -6) x⁽¹⁺⁴⁾ y⁽⁵⁺²⁾

Step 3. Simplify.

-18x⁵y⁷

Step 1. Group coefficients and like bases.

-12 ^. -3 ^. a^{2 .} a^{2 .} b^{3 .} b^{2 .} c⁴

Step 2. Multiply coefficients & apply the product rule of exponents.

(-12 ^. -3) a⁽²⁺²⁾ b⁽³⁺²⁾(c⁴)

Step 3. Simplify.

36a⁴b⁵c⁴