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# Topic 2 multiplying polynomials - part 1

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### Topic 2 multiplying polynomials - part 1

1. 1. Multiplying Polynomials Module 9 - Topic 2 Part 1
2. 2. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) by the monomial outside the parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
3. 3. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( !7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
4. 4. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( !7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) will be the same as after multiplying.
5. 5. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( !7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis ( 3x 2x ! 7x + 5 2 2 ) will be the same as 6x ! 21x + 15x 4 3 2 after multiplying.
6. 6. Multiply a Polynomial by a Monomial Review this Cool Math site to learn about multiplying a polynomial by a monomial. Do the Try It and Your Turn problems in your notebook and check your answers on the next slides.
7. 7. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 )
8. 8. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 ) Distribute the monomial.
9. 9. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 ) Distribute the monomial. 6x ! 2x + 6x ! 3 4 2 4
10. 10. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 ) Distribute the monomial. 6x ! 2x + 6x ! 3 4 2 4 Multiply each term.
11. 11. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 ) Distribute the monomial. 6x ! 2x + 6x ! 3 4 2 4 Multiply each term. 12x + 18x 6 4
12. 12. Try It - Page 1 Multiply: ( 6x 2x + 3 4 2 ) Distribute the monomial. 6x ! 2x + 6x ! 3 4 2 4 Multiply each term. 12x + 18x 6 4 Verify your answer has same number of terms as inside original ( ). Both have 2 terms.
13. 13. Your Turn - Page 2 multiply:
14. 14. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x 5 2 )
15. 15. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x 5 2 ) Distribute the monomial.
16. 16. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x5 2 ) Distribute the monomial. ( ) 10x 2x + 10x (1) + 10x !3x + 10x ( x ) 3 5 3 3 ( 2 ) 3
17. 17. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x5 2 ) ( ) 10x 2x + 10x (1) + 10x !3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 Multiply each term.
18. 18. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x !3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 Multiply each term. 20x + 10x ! 30x + 10x 8 3 5 4
19. 19. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x !3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 Put in descending 20x + 10x ! 30x + 10x 8 3 5 4 order and verify number of terms. (Both have 4 terms.)
20. 20. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 ! 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x !3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 Put in descending 20x + 10x ! 30x + 10x 8 3 5 4 order and verify number of terms. (Both have 4 terms.) 20x ! 30x + 10x + 10x 8 5 4 3
21. 21. Try It - Page 2 Multiply: 5 ( 4x w w ! x + 6xw ! 1 + 3x w 2 2 2 4 8 )
22. 22. Try It - Page 2 Multiply: 5 ( 4x w w ! x + 6xw ! 1 + 3x w 2 2 2 4 8 ) Distribute the monomial.
23. 23. Try It - Page 2 Multiply: 5 ( 4x w w ! x + 6xw ! 1 + 3x w 2 2 2 4 8 ) Distribute the monomial. 5 ( 2 ) 2 5 ( 2 ) 4x w ( w ) + 4x w !x + 4x w 6xw + 4x w ( !1) + 4x w 3x w 2 5 2 2 5 2 5 ( 4 8 )
24. 24. Try It - Page 2 Multiply: 5 ( 4x w w ! x + 6xw ! 1 + 3x w 2 2 2 4 8 ) 5 ( 2 ) 2 5 ( 2 ) 4x w ( w ) + 4x w !x + 4x w 6xw + 4x w ( !1) + 4x w 3x w 2 5 2 2 5 2 5 ( 4 8 ) Multiply each term.
25. 25. Try It - Page 2 Multiply: 5 ( 4x w w ! x + 6xw ! 1 + 3x w 2 2 2 4 8 ) 5 ( 2 ) 4x w ( w ) + 4x w !x + 4x w 6xw + 4x w ( !1) + 4x w 3x w 2 5 2 2 5 ( 2 ) 2 5 2 5 ( 4 8 ) Multiply each term. 4x w ! 4x w + 24x w ! 4x w + 12x w 2 6 4 5 3 7 2 5 6 13 Verify answer has 5 terms like original parenthesis.
26. 26. Try this one... Multiply: ( 3x 2x ! 5x + 7 2 )
27. 27. Try this one... Multiply: ( 3x 2x ! 5x + 7 2 ) Distribute the monomial.
28. 28. Try this one... Multiply: ( 3x 2x ! 5x + 7 2 ) Distribute the monomial. ( ) 3x 2x + 3x ! ( "5x ) + 3x ( 7 ) 2
29. 29. Try this one... Multiply: ( 3x 2x ! 5x + 7 2 ) ( ) 3x 2x + 3x ! ( "5x ) + 3x ( 7 ) 2 Multiply each term.
30. 30. Try this one... Multiply: ( 3x 2x ! 5x + 7 2 ) ( ) 3x 2x + 3x ! ( "5x ) + 3x ( 7 ) 2 Multiply each term. 6x ! 15x + 21x 3 2
31. 31. Try this one... Multiply: 2 2 ( !2a b a + 3a b ! 4b 3 2 3 5 )
32. 32. Try this one... Multiply: 2 2 ( !2a b a + 3a b ! 4b 3 2 3 5 ) Distribute the monomial.
33. 33. Try this one... Multiply: 2 2 ( !2a b a + 3a b ! 4b 3 2 3 5 ) Distribute the monomial. ( !2a b )( a ) + ( !2a b )( 3a b ) + ( !2a b )( !4b ) 2 2 3 2 2 2 3 2 2 5
34. 34. Try this one... Multiply: 2 2 ( !2a b a + 3a b ! 4b 3 2 3 5 ) ( !2a b )( a ) + ( !2a b )( 3a b ) + ( !2a b )( !4b ) 2 2 3 2 2 2 3 2 2 5 Multiply each term.
35. 35. Try this one... Multiply: 2 2 ( !2a b a + 3a b ! 4b 3 2 3 5 ) ( !2a b )( a ) + ( !2a b )( 3a b ) + ( !2a b )( !4b ) 2 2 3 2 2 2 3 2 2 5 Multiply each term. !2a b ! 6a b + 8a b 5 2 4 5 2 7
36. 36. Great job working all those problems! Proceed to Part 2.