Adding and Subtracting Polynomials 7-6 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n2 Simplify each expression. 5. 3(x + 4) 6. –2(t + 3) 7. –1(x2 – 4x – 6) 6x 10y 3p not like terms 3x + 12 –2t – 6 –x2 + 4x + 6

Example 1: Adding and Subtracting Monomials Add or Subtract.. A. 12p3 + 11p2 + 8p3 12p3 + 11p2 + 8p3 Identify like terms. 20p3 + 11p2 Combine like terms. B. 5x2 – 6 – 3x + 8 Identify like terms. 5x2 – 6 – 3x + 8 5x2 – 3x + 2 Combine like terms.

Example 1: Adding and Subtracting Monomials Add or Subtract.. C. t2 + 2s2 – 4t2 – s2 t2 + 2s2 – 4t2 – s2 Identify like terms. –3t2 + s2 Combine like terms. D. 10m2n + 4m2n – 8m2n 10m2n + 4m2n – 8m2n Identify like terms. 6m2n Combine like terms.

You try these! Add or subtract. a. 2s2 + 3s2 + s Ans: 5s2 + s b. 4z4 – 8 + 16z4 + 2 Ans: 20z4 – 6

Add or subtract. c. 2x8 + 7y8 – x8 – y8 Ans: x8 + 6y8 d. 9b3c2 + 5b3c2 – 13b3c2 Ans: b3c2

Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: In horizontal form, regroup and combine like terms. (5x2 + 4x + 1) + (2x2 + 5x + 2) (5x2 + 4x + 1) + (2x2 + 5x + 2) 5x2 + 4x + 1 + 2x2 + 5x + 2 7x2 + 9x + 3 = (5x2 + 2x2) + (4x + 5x) + (1 + 2) = 7x2 + 9x + 3

Add. A. (4m2 + 5) + (m2 – m + 6) Ans: 5m2 – m + 11 B. (10xy + x) + (–3xy + y) Ans: 7xy + x + y

Add. (6x2 – 4y) + (3x2 + 3y – 8x2 – 2y) Ans: x2 – 3y

Add.

You Try! Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a). Ans:12a3 + 15a2 – 16a

Subtracting Polynomials (x3 + 4y) – (2x3) Ans: –x3 + 4y

Subtract. (7m4 – 2m2) – (5m4 – 5m2 + 8) Ans: 2m4 + 3m2 – 8

Subtract. (–10x2 – 3x + 7) – (x2 – 9) Ans: –11x2 – 3x + 16

Subtract. (9q2 – 3q) – (q2 – 5) Ans: 8q2 – 3q + 5

You Try! Subtract. (2x2 – 3x2 + 1) – (x2 + x + 1) Ans: –2x2 – x

A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land. Plot A. Plot B. (3x2 + 7x – 5) + (5x2 – 4x + 11)

Lesson Quiz: Part I Add or subtract. 1. 7m2 + 3m + 4m2 2. (r2 + s2) – (5r2 + 4s2) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d2 – 8) + (6d2 – 2d +1) 5. (2.5ab + 14b) – (–1.5ab + 4b)

Lesson Quiz: Part II 6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x2 + 12x + 9, and the area of the second wall is modeled by 36x2 – 12x + 1. Write a polynomial that represents the total area of the two walls.