Adding Subtracting and Multiplying Polynomials

To simplify the expression by multiplying a binomial by a trinomial, we will apply the Distributive Property.

(- x - 3) (2 x^{2} + 5 x + 8)

MultParMultiply parentheses

- x (2 x^{2} + 5 x + 8) - 3 (2 x^{2} + 5 x + 8)

DistrDistribute

- x

- 2 x^{3} - 5 x^{2} - 8 x - 3 (2 x^{2} + 5 x + 8)

DistrDistribute

- 3

- 2 x^{3} - 5 x^{2} - 8 x - 6 x^{2} - 15 x - 24

The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable and the same exponent — can be combined.

- 2 x^{3} - 5 x^{2} - 8 x - 6 x^{2} - 15 x - 24

In this case, we have one

x^{3} - term,

two

x^{2} - terms,

two

x - terms,

and one

constant .

To simplify the expression we will rearrange the terms and then evaluate the sum or difference of the like terms.

- 2 x^{3} - 5 x^{2} - 8 x - 6 x^{2} - 15 x - 24

CommutativePropAddCommutative Property of Addition

- 2 x^{3} - 5 x^{2} - 6 x^{2} - 8 x - 15 x - 24

AddSubTermsAdd and subtract terms

- 2 x^{3} - 11 x^{2} - 14 x - 24

Adding Subtracting and Multiplying Polynomials 1.9 - Solution