4 2 ADDING SUBTRACTING AND MULTIPLYING POLYNOMIALS Adding

4. 2 ADDING, SUBTRACTING, AND MULTIPLYING POLYNOMIALS

Adding and Subtracting Polynomials �To add or subtract polynomials, you add or subtract the coefficients of like terms

Example 1 Adding Polynomials Vertically and Horizontally Organize expressions vertically and put like terms over like terms. ONLY add coefficients with like terms (e. g. 4 x 3 with x 3)

Example 2 Subtracting Polynomials Vertically and Horizontally Align like terms, then add opposite of subtracted polynomial

Example 2 cont. Subtracting Polynomials Vertically and Horizontally � Write the opposite of the subtracted polynomial, then add like terms

Multiplying Polynomials �Multiply each term of first polynomial by each term of second polynomial

Example 3 Multiply Polynomials Vertically and Horizontally Combine like terms

Example 4 Multiplying Three Binomials �

Special Product Pattern Sum and Difference Example Square of a Binomial Example Cube of a Binomial Example

Example 5 Proving a Polynomial Identity a. Prove the polynomial identity for the cube of a binomial representing a sum : SOLUTION Expand simplify the expression on the left side of the equation b. Use the cube of the binomial in part (a) to calculate 113 SOLUTION Cube of a binomial Expand ✔ Simplify

Example 6 Using Special Product Patterns Find each Product Sum and difference Cube of a binomial Simplify Square of a binomial Simplify

Pascal’s Triangle Numbers in Pascal’s Triangle are same numbers that are coefficients of binomial expansions: Binomial Expansion Pascal’s Triangle = = = 1 1 1 2 3 4 5 1 1 3 6 10 1 4 10 1 5 1

Using Pascal’s Triangle to Expand Binomials � Pascal’s Triangle Example 8 1 1 1 SOLUTION 1 1 1 2 3 4 5 1 1 3 6 10 1 4 10 1 5 1

Example 8 Pascal’s Triangle SOLUTION 1 1 1 2 3 4 5 1 1 3 6 10 1 4 10 1 5 1

Example 9 Pascal’s Triangle 1 1 1 2 3 4 5 1 1 3 6 10 1 4 10 1 5 1