Adding Subtracting and Multiplying Polynomials

To multiply these two trinomials, we will use the Distributive Property.

(x^{2} - 2 x - 4) (x^{2} - 3 x - 5)

MultParMultiply parentheses

x^{2} (x^{2} - 3 x - 5) - 2 x (x^{2} - 3 x - 5) - 4 (x^{2} - 3 x - 5)

DistrDistribute

x^{2}

x^{4} - 3 x^{3} - 5 x^{2} - 2 x (x^{2} - 3 x - 5) - 4 (x^{2} - 3 x - 5)

DistrDistribute

- 2 x

x^{4} - 3 x^{3} - 5 x^{2} - 2 x^{3} + 6 x^{2} + 10 x - 4 (x^{2} - 3 x - 5)

DistrDistribute

- 4

x^{4} - 3 x^{3} - 5 x^{2} - 2 x^{3} + 6 x^{2} + 10 x - 4 x^{2} + 12 x + 20

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.

x^{4} - 3 x^{3} - 5 x^{2} - 2 x^{3} + 6 x^{2} + 10 x - 4 x^{2} + 12 x + 20

In this case, we have one

x^{4} - term,

two

x^{3} - terms,

three

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.

x^{4} - 3 x^{3} - 5 x^{2} - 2 x^{3} + 6 x^{2} + 10 x - 4 x^{2} + 12 x + 20

CommutativePropAddCommutative Property of Addition

x^{4} - 3 x^{3} - 2 x^{3} - 5 x^{2} - 4 x^{2} + 6 x^{2} + 10 x + 12 x + 20

AddSubTermsAdd and subtract terms

x^{4} - 5 x^{3} - 3 x^{2} + 22 x + 20

Adding Subtracting and Multiplying Polynomials 1.11 - Solution