Page 680 #20-24 Pre-Algebra HOMEWORK Adding Polynomials 13-3

Pre-Algebra 13-1 Polynomials Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials.

Pre-Algebra 13-1 Polynomials Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments. Learn to classify polynomials by degree and by the number of terms. Learn to simplify polynomials. Learn to add polynomials. Learn to subtract polynomials. …..and that’s all folks!

Today’s Learning Goal Assignment Pre-Algebra 13-3 Adding Polynomials Today’s Learning Goal Assignment Learn to add polynomials.

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

Adding Polynomials 13-3 Warm Up Combine like terms. Pre-Algebra 13-3 Adding Polynomials Warm Up Combine like terms. 1. 9x + 4x 2. –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(2x2 – x) + x2+ 1 13x 4y 11n 44 ft 26 m 7x2 – 3x + 1

Adding Polynomials 13-3 Problem of the Day Pre-Algebra 13-3 Adding Polynomials 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.

Additional Example 1A: Adding Polynomials Horizontally Pre-Algebra 13-3 Adding Polynomials Additional Example 1A: Adding Polynomials Horizontally Add. A. (5x3 + x2 + 2) + (4x3 + 6x2) (5x + x + 2) + (4x + 6x ) 3 2 5x + x + 2 + 4x + 6x 3 2 Associative Property 9x + 7x + 2 3 2 Combine like terms.

Adding Polynomials 13-3 Try This: Example 1A Add. Pre-Algebra 13-3 Adding Polynomials Try This: Example 1A Add. A. (3y4 + y2 + 6) + (5y4 + 2y2) (3y + y + 6) + (5y + 2y ) 4 2 3y + y + 6 + 5y + 2y 4 2 Associative Property 8y + 3y + 6 4 2 Combine like terms.

Additional Example 1B: Adding Polynomials Horizontally Pre-Algebra 13-3 Adding Polynomials Additional Example 1B: Adding Polynomials Horizontally Add. B. (6x3+ 8y2 + 5xy) + (4xy – 2y2) (6x3+ 8y2+ 5xy) + (4xy – 2y2) 6x3 + 8y2 + 5xy + 4xy – 2y2 Associative Property 6x + 6y + 9xy 3 2 Combine like terms.

Adding Polynomials 13-3 Try This: Example 1B Add. Pre-Algebra 13-3 Adding Polynomials Try This: Example 1B Add. B. (9x3 + 6p2 + 3xy) + (8xy – 3p2) (9x + 6p + 3xy) + (8xy – 3p ) 3 2 9x + 6p + 3xy + 8xy – 3p 3 2 Associative Property 9x3+ 3p2+ 11xy Combine like terms.

Additional Example 1C: Adding Polynomials Horizontally Pre-Algebra 13-3 Adding Polynomials Additional Example 1C: Adding Polynomials Horizontally Add. C. (3x2y – 5x) + (4x + 7) + 6x2y (3x2y – 5x) + (4x + 7) + 6x2y 3x2y – 5x + 4x + 7 + 6x2y Associative Property 9x2y – x + 7 Combine like terms.

Adding Polynomials 13-3 Try This: Example 1C Add. Pre-Algebra 13-3 Adding Polynomials Try This: Example 1C Add. C. (3z2w – 5x) + (2x + 8) + 6z2w (3z2w – 5x) + (2x + 8) + 6z2w 3z2w – 5x + 2x + 8 + 6z2w Associative Property 9z2w – 3x + 8 Combine like terms.

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.

Additional Example 2A: Adding Polynomials Vertically Pre-Algebra 13-3 Adding Polynomials Additional Example 2A: Adding Polynomials Vertically Add. A. (4x2 + 2x + 11) + (2x2 + 6x + 9) 4x2 + 2x + 11 + 2x2 + 6x + 9 Place like terms in columns. 6x2 + 8x + 20 Combine like terms.

Adding Polynomials 13-3 Try This: Example 2A Add. Pre-Algebra 13-3 Adding Polynomials Try This: Example 2A Add. A. (6x2 + 6x + 13) + (3x2+ 2x + 4) 6x2 + 6x + 13 + 3x2 + 2x + 4 Place like terms in columns. 9x2 + 8x + 17 Combine like terms.

Additional Example 2B & 2C: Adding Polynomials Vertically Pre-Algebra 13-3 Adding Polynomials Additional Example 2B & 2C: Adding Polynomials Vertically Add. B. (3mn2 – 6m + 6n) + (5mn2 + 2m – 6n) C. (–x2y2 + 5x2) + (–2y2 + 2) + (x2 + 8) 3mn2 – 6m + 6n + 5mn2 + 2m – n Place like terms in columns. 8mn2 – 4m + 5n Combine like terms. –x2y2 + 5x2 –2y2 + 2 Place like terms in columns. + x2 + 8 –x2y2 + 6x2 – 2y2 +10 Combine like terms.

Adding Polynomials 13-3 Try This: Example 2B & 2C Add. Pre-Algebra 13-3 Adding Polynomials Try This: Example 2B & 2C Add. B. (4mn2 + 6m + 2n) + (2mn2 – 2m – 2n) C. (x2y2 – 5x2) + (2y2 – 2) + (x2) 4mn2 + 6m + 2n + 2mn2 – 2m – 2n Place like terms in columns. 6mn2 + 4m Combine like terms. x2y2 – 5x2 2y2 – 2 Place like terms in columns. + x2 x2y2 – 4x2 + 2y2 – 2 Combine like terms.

Additional Example 3: Application Pre-Algebra 13-3 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, and the width of the wood is 1 inches. Find an expression for the length of wood she needs to frame both photographs. 1 2

Additional Example 3 Continued Pre-Algebra 13-3 Adding Polynomials Additional Example 3 Continued Perimeter of photograph 1: Perimeter of photograph 2: P = 2b + 2h + 12 P = 4b + 4h + 12 P = (2b + 2h + 12) + (4b + 4h + 12) = 2b + 2h + 12 + 4b + 4h + 12 = 6b + 6h + 24 Combine like terms. She will need 6b + 6h + 24 in. of wood.

Adding Polynomials 13-3 Try This: Example 3 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.

Try This: Example 3 Continued Pre-Algebra 13-3 Adding Polynomials Try This: Example 3 Continued Perimeter of photograph 1: Perimeter of photograph 2: P = 2b + 2h + 16 P = 6b + 6h + 16 P = (2b + 2h + 16) + (6b + 6h + 16) = 2b + 2h + 16 + 6b + 6h + 16 = 8b + 8h + 32 Combine like terms. He will need 8b + 8h + 32 in. of wood.

Insert Lesson Title Here Pre-Algebra 13-3 Adding Polynomials Insert Lesson Title Here Lesson Quiz: Part 1 Add. 1. (2m2 – 3m + 7) + (7m2 – 1) 2. (yz2 + 5yz + 7) + (2yz2 – yz) 3. 9m2 – 3m + 6 3yz2+ 4yz + 7 (2xy2 + 2x – 6) + (5xy2 + 3y + 8) 7xy + 2x + 3y + 2 2

Insert Lesson Title Here Pre-Algebra 13-3 Adding Polynomials Insert Lesson Title Here Lesson Quiz: Part 2 4. (3np3 + 4n) (5np3 – 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. 8np3 + 5n – 9 7x + 2y+ 4