Name ________________________________________ Date __________________ Class __________________ Adding Polynomial Expressions LESSON 4-2 Reteach You can add polynomials by combining like terms. These are examples of like terms: 4y and 7y 8x2 and 2x2 m5 and 7m5 These are like terms because they have the same variables and same exponent. These are not like terms: Add (5y2 + 7y + 2) + (4y2 + y + 8). (5y2 + 7y + 2 ) + (4y2 + y + 8 ) 2 2 (5y + 4y ) + ( 7y + y ) + ( 2 + 8 ) 2 9y + 8y + 10 3x2 and 3x 4y and 7 same variable but different exponent one with a variable, one is a constant 8m and 8n different variables Identify like terms. Rearrange terms so that like terms are together. Combine like terms. Add (5y2 + 7y + 2) + (4y2 + y + 8). (5y2 + 7y + 2 ) + (4y2 + y + 8 ) Identify like terms. (5y2 + 4y2) + ( 7y + y ) + ( 2 + 8 ) Rearrange terms so that like terms are together. 9y2 + 8y + 10 Combine like terms. Add. 1. (6x2 + 3x) + (2x2 + 6x) ____________________________________________________ 2. (m2 − 10m + 5) + (8m + 2) ____________________________________________________ 3. (6x3 + 5x) + (4x3 + x2 − 2x + 9) ____________________________________________________ 4. (2y5 − 6y3 + 1) + (y5 + 8y4 − 2y3 − 1) ____________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 85 Name ________________________________________ Date __________________ Class __________________ LESSON 4-2 Adding Polynomial Expressions Practice and Problem Solving: Modified Add. The first one is done for you. 1. 2m + 4 2. 3m + 6 ________________________ 12k + 3 + 4k + 2 ________________________ 3. + 2y 2 + 2y + 9 +m+2 4. 3y 2 − y + 3 + 2z 3 + z 2 − 3 _______________________ 5. 6s 3 + 9s + 10 ________________________ 6. + 3s 3 + 4s − 10 15a 4+ 6a 2+a + 6a 4 − 2a 2 + a _______________________ 7. (3x3 + 4) + (x3 − 10) 4z 3 + 3z 2 + 8 ________________________ 8. (10g 2 + 3g − 10) + (2g 2 + g + 9) ________________________________________ ________________________________________ 9. (12p5 + 8) + (8p5 + 6) 10. (11b 2 + 3b − 1) + (2b 2 + 2b + 8) ________________________________________ ________________________________________ Solve. The first one is started for you. 11. Rebecca is building a pen for her rabbits against the side of her house. The polynomial 4n + 8 represents the length and the polynomial 2n + 6 represents the width. a. What polynomial represents the perimeter of the entire pen? (4n + 8) + (4n + 8 ) + (2n + 6) + (2n + 6) = _________________________________________ ________________________________________ b. What polynomial represents the perimeter of the pen NOT including the side of the house. ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 51 Name ________________________________________ Date __________________ Class __________________ LESSON 4-2 Adding Polynomial Expressions Practice and Problem Solving: A/B Add the polynomial expressions using the vertical format. 1. (10g 2 + 3g − 10) 2. + (2g 2 + g + 9) ________________________________________ 3. + (3 x 3 + x 2 + 4 x ) ________________________________________ (11b 2 + 3b − 1) 4. + (2b 2 + 2b + 8) ________________________________________ 5. (4 x 3 + x 2 + 2 x ) ( c 3 + 2c 2 + 2c ) + ( −3c 3 + c 2 − 4c ) ________________________________________ (ab 2 + 13b − 4a ) 6. + (3ab 2 + a + 7b ) ________________________________________ ( −r 2 + 8 pr − p ) + ( −12r 2 − 2 pr + 8 p ) ________________________________________ Add the polynomial expressions using the horizontal format. 7. (3y2 − y + 3) + (2y2 + 2y + 9) 8. (4z3 + 3z2 + 8) + (2z3 + z2 − 3) ________________________________________ ________________________________________ 9. (6s3 + 9s + 10) + (3s3 + 4s − 10) 10. (15a4 + 6a2 + a) + (6a4 − 2a2 + a) ________________________________________ ________________________________________ 11. (−7a2b3 + 3a3b − 9ab) + (4a2b3 − 5a3b + ab) ________________________________________ 12. (2p4q2 + 5p3q − 2pq) + (8p4q2 − 3p3q − pq) ________________________________________ Solve. 13. A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame. _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 49 Int Math 2 Name___________________________________ Adding Polynomials Simplify each sum. 1) ( x 2 + 2) + (2 − 3x 3 − 8x 2 ) 2) (8x 4 − 7x 3 ) + (2x 3 + 2x 2 − 2x 4 ) 3) (2x 4 − 8) + (8x 4 + 7 + 2x) 4) (8k + 1) + (3k 2 + 3 − 2k) 5) (3 − 8n 4 ) + (3n 4 − 2n 3 + 6) 6) (4r 2 + 3r) + (8r + 4r 4 + 2r 2 ) 7) (7n 3 + 7) + (6n 2 − 6 − 5n 3 ) 8) (a 2 − 8) + (8a 2 + 5a 3 + 3) 9) (6x + x 2 ) + (7x − 1 − 5x 2 ) 10) (2x 4 + 7x 2 ) + (3x 2 + 3x 4 − 5x) Worksheet by Kuta Software LLC ©F p2k0A1K5Y uKkuGtyap HSfoFfjtRwlarrTej ]LFLxC\.S D cA[lHl^ lrNitgohMtfsw VrPeCsMeZrfvuezde.` n JMkaPdyeg Ew[iDtchq pIwnBfaiinKiAtBeg eA\lEgseJbCrKan I2F.