7 6 Adding and Subtracting Polynomials Objective Add

7 -6 Adding and Subtracting Polynomials Objective Add and subtract polynomials. Holt Algebra 1

7 -6 Adding and Subtracting Polynomials Example 1: Adding and Subtracting Monomials Add or Subtract only monomials with the exact same letters AND exponents. A. 12 p 3 + 11 p 2 + 8 p 3 12 p 3 + 8 p 3 + 11 p 2 20 p 3 + 11 p 2 B. 5 x 2 – 6 – 3 x + 3 x 2 + 8 5 x 2 + 3 x 2 – 6 – 3 x + 8 8 x 2 – 3 x + 8 – 6 8 x 2 – 3 x + 2 Holt Algebra 1 Identify like terms. Rearrange terms so that like terms are together. Combine like terms.

7 -6 Adding and Subtracting Polynomials Example 1: Adding and Subtracting Monomials Add or Subtract only monomials with the exact same letters AND exponents. C. t 2 + 2 s 2 – 4 t 2 – s 2 t 2 – 4 t 2 + 2 s 2 – 3 t 2 + s 2 Identify like terms. Rearrange terms so that like terms are together. Combine like terms. D. 10 m 2 n + 4 m 2 n – 8 m 2 n Identify like terms. 6 m 2 n Combine like terms. Holt Algebra 1

7 -6 Adding and Subtracting Polynomials Check It Out! Example 1 Add or Subtract only monomials with the exact same letters AND exponents. c. 2 x 6 + 7 y 8 – x 6 + y 2 2 x 6 + 7 y 8 – x 6 – y 2 2 x 6 – x 6 + 7 y 8 – y 2 Identify like terms. Rearrange terms so that like terms are together. Combine like terms. d. 9 b 3 c 2 + 5 b 3 c 2 – 10 b 2 c 2 14 b 3 c 2 – 10 b 2 c 2 Holt Algebra 1 Identify like terms. Combine like terms.

7 -6 Adding and Subtracting Polynomials Example 2: Adding Polynomials Add or Subtract only monomials with the exact same letters AND exponents. A. (4 m 2 + 5) + (m 2 – m + 6) Identify like terms. (4 m 2 + m 2) + (–m) + (5 + 6) Group like terms together. Combine like terms. 5 m 2 – m + 11 B. (10 xy + x + 3 y) + (– 3 xy + y) Identify like terms. Group like terms 10 xy – 3 xy + x + 3 y + y together. 7 xy + x + 4 y Combine like terms. Holt Algebra 1

7 -6 Adding and Subtracting Polynomials Check It Out! Example 2 Add or Subtract only monomials with the exact same letters AND exponents. Add (5 a 3 + 3 a 2 – 6 a + 12 a 2) + (7 a 3 – 10 a) Identify like terms. 5 a 3 + 7 a 3 + 3 a 2 + 12 a 2 – 10 a – 6 a Group like terms together. 12 a 3 + 15 a 2 – 16 a Holt Algebra 1 Combine like terms

7 -6 Adding and Subtracting Polynomials Example 3 B: Subtracting Polynomials Subtract. DISTRIBUTE THE NEGATIVE (7 m 4 – 2 m 2) – (5 m 4 – 5 m 2 + 8) Distribute a -1 to everything (7 m 4 – 2 m 2) + (– 5 m 4 + 5 m 2 – 8) in the second set of parentheses. 7 m 4 – 2 m 2 – 5 m 4 + 5 m 2 – 8 7 m 4 – 5 m 4 – 2 m 2 + 5 m 2 – 8 2 m 4 + 3 m 2 – 8 Holt Algebra 1 Identify like terms. Group like terms together. Combine like terms.

7 -6 Adding and Subtracting Polynomials Example 3 D: Subtracting Polynomials Subtract. DISTRIBUTE THE NEGATIVE (9 q 2 – 3 q) – (q 2 – 5 - 3) Distribute a -1 to everything (9 q 2 – 3 q) + (–q 2 + 5 + 3) in the second set of parentheses. Identify like terms. 9 q 2 – 3 q –q 2 + 5 + 3 Use the vertical method. 9 q 2 – 3 q + 5 + 3 8 q 2 – 3 q + 8 Holt Algebra 1 Combine like terms.