13-3 Adding Polynomials Pre-Algebra Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up 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 Pre-Algebra 13-3 Adding Polynomials 44 ft 26 m 7x 2 – 3x + 1

Problem of the Day Michael has a collection of dimes and quarters worth $6.55. If he has one more quarter than he has dimes, how many of each coin does he have? 18 dimes and 19 quarters Pre-Algebra 13-3 Adding Polynomials

Learn to add polynomials. Pre-Algebra 13-3 Adding Polynomials

Additional Example 1A: Adding Polynomials Horizontally 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. Pre-Algebra 13-3 Adding Polynomials

Additional Example 1B: 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. Pre-Algebra 13-3 Adding Polynomials

Additional Example 1C: 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 Pre-Algebra 13-3 Adding Polynomials

Try This: Example 1A 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. Pre-Algebra 13-3 Adding Polynomials

Try This: Example 1B 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. Pre-Algebra 13-3 Adding Polynomials

Try This: Example 1C 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 Pre-Algebra 13-3 Adding Polynomials

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. Pre-Algebra 13-3 Adding Polynomials

Additional Example 2A: Adding Polynomials Vertically Add. A. (4x 2 + 2x + 11) + (2x 2 + 6x + 9) 4x 2 + 2x x 2 + 6x + 9 6x 2 + 8x + 20 Pre-Algebra 13-3 Adding Polynomials Combine like terms. Place like terms in columns.

Additional Example 2B & 2C: 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 Pre-Algebra 13-3 Adding Polynomials Combine like terms. Place like terms in columns. Combine like terms. Place like terms in columns.

Try This: Example 2A Add. A. (6x 2 + 6x + 13) + (3x 2 + 2x + 4) Pre-Algebra 13-3 Adding Polynomials 6x 2 + 6x x 2 + 2x + 4 9x 2 + 8x + 17 Combine like terms. Place like terms in columns.

Try This: Example 2B & 2C Add. B. (4mn 2 + 6m + 2n) + (2mn 2 – 2m – 2n) C. (x 2 y 2 – 5x 2 ) + (2y 2 – 2) + (x 2 ) Pre-Algebra 13-3 Adding Polynomials + 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.

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, and the width of the wood is 1 inches. Find an expression for the length of wood she needs to frame both photographs. Pre-Algebra 13-3 Adding Polynomials 1212

Additional Example 3 Continued = 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: Pre-Algebra 13-3 Adding Polynomials

Try This: 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. Pre-Algebra 13-3 Adding Polynomials

Try This: Example 3 Continued = 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: Pre-Algebra 13-3 Adding Polynomials

Lesson Quiz: Part 1 Add. 1. (2m 2 – 3m + 7) + (7m 2 – 1) 2. (yz 2 + 5yz + 7) + (2yz 2 – yz) 3. Insert Lesson Title Here 9m 2 – 3m + 6 3yz 2 + 4yz + 7 7xy + 2x + 3y Pre-Algebra 13-3 Adding Polynomials (2xy 2 + 2x – 6) + (5xy 2 + 3y + 8)

Lesson Quiz: Part 2 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 Insert Lesson Title Here 8np 3 + 5n – 9 Pre-Algebra 13-3 Adding Polynomials