##### Example 1

Let's multiply the polynomial (3x^{2} + 2) by the monomial 5x .

You should be comfortable combining like terms and using the laws of exponents.

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Examples, steps and problems

Let's multiply the polynomial (3x^{2} + 2) by the monomial 5x .

You should be comfortable combining like terms and using the laws of exponents.

on Multiplying Monomials by Polynomials

This problem is similar to example 1.

Step 1Distribute by multiplying the monomial with every term in the polynomial.

Step 2

Simplify using the formula for multiplying exponents
21x^{4} + 28x^{3} - 35x.

Step 1

Distribute by multiplying the monomial with every term in the polynomial.

Step 2

Simplify using the formula for multiplying exponents
45x^{5} − 36x^{12} + 108x.

Step 1

Distribute by multiplying the monomial with every term in the polynomial.

Step 2

Simplify using the formula for multiplying exponents
10x^{12} − 45x^{11} + 20x^{4}.

Step 1

Distribute by multiplying the monomial with every term in the polynomial.

Step 2

Simplify using the formula for multiplying exponents
-6x^{8} − 18x^{6} − 8x.