12 3 Adding Polynomials Preview Warm Up California

12 -3 Adding Polynomials Preview Warm Up California Standards Lesson Presentation Holt CA Course 1

12 -3 Adding Polynomials Warm Up Combine like terms. 1. 9 x + 4 x 13 x 2. – 3 y + 7 y 4 y 3. 7 n + (– 8 n) + 12 n 11 n Find the perimeter of each rectangle. 4. a 10 ft by 12 ft rectangle 44 ft 5. a 5 m by 8 m rectangle 26 m Simplify. 6. 3(2 x 2 – x) + x 2+ 1 Holt CA Course 1 7 x 2 – 3 x + 1

12 -3 Adding Polynomials California Standards Preview of Algebra 1 10. 0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7 AF 1. 3 Holt CA Course 1

12 -3 Adding Polynomials Additional Example 1: Adding Polynomials Horizontally Add. A. (5 x 3 + x 2 + 2) + (4 x 3 + 6 x 2) 5 x 3 + x 2 + 4 x 3 + 6 x 2 Write as one polynomial. 5 x 3 + 4 x 3 + x 2 + 6 x 2 + 2 Commutative Property 9 x 3 + 7 x 2 + 2 Combine like terms. Holt CA Course 1

12 -3 Adding Polynomials Additional Example 1: Adding Polynomials Horizontally Add. B. (6 x 3+ 8 y 2 + 5 xy) + (4 xy – 2 y 2) 6 x 3 + 8 y 2 + 5 xy + 4 xy – 2 y 2 Write as one polynomial. 6 x 3 + 8 y 2 – 2 y 2 + 5 xy + 4 xy Commutative Property 6 x 3 + 6 y 2 + 9 xy Holt CA Course 1 Combine like terms.

12 -3 Adding Polynomials Additional Example 1: Adding Polynomials Horizontally Add. C. (3 x 2 y – 5 x) + (4 x + 7) + 6 x 2 y 3 x 2 y – 5 x + 4 x + 7 + 6 x 2 y Write as one polynomial. 3 x 2 y + 6 x 2 y – 5 x + 4 x + 7 Commutative Property 9 x 2 y – x + 7 Holt CA Course 1 Combine like terms.

12 -3 Adding Polynomials Check It Out! Example 1 Add. A. (3 y 4 + y 2 + 6) + (5 y 4 + 2 y 2) 3 y 4 + y 2 + 6 + 5 y 4 + 2 y 2 Write as one polynomial. 3 y 4 + 5 y 4 + y 2 + 2 y 2 + 6 Commutative Property 8 y 4 + 3 y 2 + 6 Holt CA Course 1 Combine like terms.

12 -3 Adding Polynomials Check It Out! Example 1 Add. B. (9 x 3 + 6 p 2 + 3 xy) + (8 xy – 3 p 2) 9 x 3 + 6 p 2 + 3 xy + 8 xy – 3 p 2 Write as one polynomial. 9 x 3 + 6 p 2 – 3 p 2 + 3 xy + 8 xy Commutative Property 9 x 3 + 3 p 2 + 11 xy Holt CA Course 1 Combine like terms.

12 -3 Adding Polynomials Check It Out! Example 1 Add. C. (3 z 2 w – 5 x) + (2 x + 8) + 6 z 2 w 3 z 2 w – 5 x + 2 x + 8 + 6 z 2 w Write as one polynomial. 3 z 2 w + 6 z 2 w – 5 x + 2 x + 8 Commutative Property 9 z 2 w – 3 x + 8 Holt CA Course 1 Combine like terms.

12 -3 Adding Polynomials You can also add polynomials in a vertical format. Write the second polynomial below the first one. Be sure to line up the like terms. If the terms are rearranged, remember to keep the correct sign with each term. Holt CA Course 1

12 -3 Adding Polynomials Additional Example 2: Adding Polynomials Vertically Add. A. (4 x 2 + 2 x + 11) + (2 x 2 + 6 x + 9) 4 x 2 + 2 x + 11 + 2 x 2 + 6 x + 9 6 x 2 + 8 x + 20 Holt CA Course 1 Place like terms in columns. Combine like terms.

12 -3 Adding Polynomials Additional Example 2: Adding Polynomials Vertically Add. B. (3 mn 2 – 6 m + 6 n) + (5 mn 2 + 2 m – n) 3 mn 2 – 6 m + 6 n + 5 mn 2 + 2 m – n Place like terms in columns. Combine like terms. 8 mn 2 – 4 m + 5 n C. (–x 2 y 2 + 5 x 2) + (– 2 y 2 + 2) + (x 2 + 8) –x 2 y 2 + 5 x 2 – 2 y 2 + x 2 +8 –x 2 y 2 + 6 x 2 – 2 y 2 + 10 Holt CA Course 1 Place like terms in columns. Combine like terms.

12 -3 Adding Polynomials Check It Out! Example 2 Add. A. (6 x 2 + 6 x + 13) + (3 x 2 + 2 x + 4) 6 x 2 + 6 x + 13 + 3 x 2 + 2 x + 4 9 x 2 + 8 x + 17 Holt CA Course 1 Place like terms in columns. Combine like terms.

12 -3 Adding Polynomials Check It Out! Example 2 Add. B. (4 mn 2 + 6 m + 2 n) + (2 mn 2 – 2 m – 2 n) 4 mn 2 + 6 m + 2 n + 2 mn 2 – 2 m – 2 n Place like terms in columns. 6 mn 2 + 4 m Combine like terms. C. (x 2 y 2 – 5 x 2) + (2 y 2 – 2) + (x 2) x 2 y 2 – 5 x 2 2 y 2 – 2 Place like terms in columns. + x 2 y 2 – 4 x 2 + 2 y 2 – 2 Combine like terms. Holt CA Course 1

12 -3 Adding Polynomials Additional Example 3: Application Rachel wants to frame two photographs. The first photograph has dimensions b inches and h inches, and each dimension of the other photograph is twice the corresponding dimension of the first. She needs enough wood for the frames to cover both perimeters, 1 and the width of the wood is 1 inches. Find an 2 expression for the length of wood she needs to frame both photographs. Holt CA Course 1

12 -3 Adding Polynomials Additional Example 3 Continued Perimeter of photograph 1: Perimeter of photograph 2: P = 2 b + 2 h + 12 P = 4 b + 4 h + 12 P = (2 b + 2 h + 12) + (4 b + 4 h + 12) P = 2 w + 2 l = 2 b + 2 h + 12 + 4 b + 4 h + 12 = 6 b + 6 h + 24 Combine like terms. She will need 6 b + 6 h + 24 in. of wood. Holt CA Course 1

12 -3 Adding Polynomials Check It Out! Example 3 Michael wants to frame two photographs. The first photograph had dimensions b inches and h inches, and each dimension of the other photograph is three times the corresponding dimension of the first. He needs enough wood for the frames to cover both perimeters and the width of the wood is 2 inches. Find an expression for the length of wood he will need to frame both photographs. Holt CA Course 1

12 -3 Adding Polynomials Check It Out! Example 3 Continued Perimeter of photograph 1: Perimeter of photograph 2: P = 2 b + 2 h + 16 P = 6 b + 6 h + 16 P = (2 b + 2 h + 16) + (6 b + 6 h + 16) P = 2 w + 2 l = 2 b + 2 h + 16 + 6 b + 6 h + 16 = 8 b + 8 h + 32 Combine like terms. He will need 8 b + 8 h + 32 in. of wood. Holt CA Course 1

12 -3 Adding Polynomials Add. Lesson Quiz 1. (2 m 2 – 3 m + 7) + (7 m 2 – 1) 9 m 2 – 3 m + 6 2. (yz 2 + 5 yz + 7) + (2 yz 2 – yz) 3 yz 2+ 4 yz + 7 3. (2 xy 2 + 2 x – 6) + (5 xy 2 + 3 y + 8) 7 xy 2 + 2 x + 3 y + 2 4. (3 np 3 + 4 n) + (5 np 3 – n – 6) + (2 n – 3) 8 np 3 + 5 n – 9 5. The base of an isosceles triangle has length x + 4. The two legs of the triangle have lengths 3 x + y. Write an expression for the perimeter of the triangle. 7 x + 2 y + 4 Holt CA Course 1