Combine like terms. 1. 9x + 4x2. –3y + 7y 3. 7n + (–8n) + 12n Find the perimeter of each rectangle. 4. a 10 ft by 12 ft rectangle 5. a 5 m by 8 m rectangle Simplify. 6. 3(2x 2 – x) + x x 4y4y 11n 44 ft 26 m 7x 2 – 3x + 1 Warm Up

Pre-Algebra Adding Polynomials 13-3

Learn to add polynomials.

Add. A. (5x 3 + x 2 + 2) + (4x 3 + 6x 2 ) (5x + x + 2) + (4x + 6x ) x + x x + 6x x + 7x Associative PropertyCombine like terms. Example: Adding Polynomials Horizontally

Add. B. (6x 3 + 8y 2 + 5xy) + (4xy – 2y 2 ) (6x 3 + 8y 2 + 5xy) + (4xy – 2y 2 ) 6x 3 + 8y 2 + 5xy + 4xy – 2y 2 6x + 6y + 9xy 3 2 Associative PropertyCombine like terms. Example: Adding Polynomials Horizontally

Add. C. (3x 2 y – 5x) + (4x + 7) + 6x 2 y (3x 2 y – 5x) + (4x + 7) + 6x 2 y 9x 2 y – x + 7 Associative PropertyCombine like terms. 3x 2 y – 5x + 4x x 2 y Example: Adding Polynomials Horizontally

Add. A. (3y 4 + y 2 + 6) + (5y 4 + 2y 2 ) (3y + y + 6) + (5y + 2y ) y + y y + 2y y + 3y Associative PropertyCombine like terms. Try This

Add. B. (9x 3 + 6p 2 + 3xy) + (8xy – 3p 2 ) (9x + 6p + 3xy) + (8xy – 3p ) x + 6p + 3xy + 8xy – 3p x 3 + 3p xy Associative PropertyCombine like terms. Try This

Add. C. (3z 2 w – 5x) + (2x + 8) + 6z 2 w (3z 2 w – 5x) + (2x + 8) + 6z 2 w 9z 2 w – 3x + 8 Associative PropertyCombine like terms. 3z 2 w – 5x + 2x z 2 w Try This

You can also add polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms. If the terms are rearranged, remember to keep the correct sign with each term.

Add. A. (4x 2 + 2x + 11) + (2x 2 + 6x + 9) 4x 2 + 2x x 2 + 6x + 9 6x 2 + 8x + 20 Combine like terms. Place like terms in columns. Example: Adding Polynomials Vertically

Add. B. (3mn 2 – 6m + 6n) + (5mn 2 + 2m – 6n) C. (–x 2 y 2 + 5x 2 ) + (–2y 2 + 2) + (x 2 + 8) + 5mn 2 + 2m – n 8mn 2 – 4m + 5n –2y x –x 2 y 2 + 6x 2 – 2y mn 2 – 6m + 6n –x 2 y 2 + 5x 2 Combine like terms. Place like terms in columns. Combine like terms. Place like terms in columns. Example: Adding Polynomials Vertically

Add. A. (6x 2 + 6x + 13) + (3x 2 + 2x + 4) 6x 2 + 6x x 2 + 2x + 4 9x 2 + 8x + 17 Combine like terms. Place like terms in columns. Try This

Add. B. (4mn 2 + 6m + 2n) + (2mn 2 – 2m – 2n) C. (x 2 y 2 – 5x 2 ) + (2y 2 – 2) + (x 2 ) + 2mn 2 – 2m – 2n 6mn 2 + 4m 4mn 2 + 6m + 2n Combine like terms. Place like terms in columns. 2y 2 – 2 + x 2 x 2 y 2 – 4x 2 + 2y 2 – 2 x 2 y 2 – 5x 2 Combine like terms. Place like terms in columns. Try This

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, and the width of the wood is 1 inches. Find an expression for the length of wood she needs to frame both photographs Example: Application

= 6b + 6h + 24 P = 2b + 2h + 12P = 4b + 4h + 12 P = (2b + 2h + 12) + (4b + 4h + 12) = 2b + 2h b + 4h + 12 She will need 6b + 6h + 24 in. of wood. Combine like terms. Perimeter of photograph 1:Perimeter of photograph 2: Example Continued

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. Try This

= 8b + 8h + 32 P = 2b + 2h + 16P = 6b + 6h + 16 P = (2b + 2h + 16) + (6b + 6h + 16) = 2b + 2h b + 6h + 16 He will need 8b + 8h + 32 in. of wood. Combine like terms. Perimeter of photograph 1:Perimeter of photograph 2: Try This Continued

Add. 1. (2m 2 – 3m + 7) + (7m 2 – 1) 2. (yz 2 + 5yz + 7) + (2yz 2 – yz) 3. 9m 2 – 3m + 6 3yz 2 + 4yz + 7 7xy + 2x + 3y (2xy 2 + 2x – 6) + (5xy 2 + 3y + 8) Lesson Quiz: Part 1

4. (3np 3 + 4n) (5np 3 – n – 6) + (2n – 3) 5. The base of an isosceles triangle has length x + 4. The two legs of the triangle have lengths 3x + y. Write an expression for the perimeter of the triangle. 7x + 2y+ 4 8np 3 + 5n – 9 Lesson Quiz: Part 2