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Module 9 Topic 2   multiplying polynomials - part 1
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Module 9 Topic 2 multiplying polynomials - part 1

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    • 1. Multiplying Polynomials Module 9 - Topic 2 Part 1
    • 2. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 2 3x 2x − 7x + 5 ) by the monomial outside the parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
    • 3. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) 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. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) 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.
    • 5. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis 2 ( 3x 2x − 7x + 5 2 ) will be the same as after multiplying.
    • 6. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis 2 ( 3x 2x − 7x + 5 2 ) will be the same as 4 6x − 21x + 15x 3 2 after multiplying.
    • 7. 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.
    • 8. Try It - Page 1 Multiply: 4 ( 6x 2x + 32 )
    • 9. Try It - Page 1 Multiply: 4 ( 6x 2x + 32 ) Distribute the monomial.
    • 10. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3
    • 11. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term.
    • 12. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term. 6 4 12x + 18x
    • 13. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term. 6 4 12x + 18x Verify your answer has same number of terms as inside original ( ). Both have 2 terms.
    • 14. Your Turn - Page 2 multiply:
    • 15. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x )
    • 16. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x ) Distribute the monomial.
    • 17. 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
    • 18. 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.
    • 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 Multiply each term. 8 3 5 4 20x + 10x − 30x + 10x
    • 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 8 3 5 4 Put in descending 20x + 10x − 30x + 10x order and verify number of terms. (Both have 4 terms.)
    • 21. 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 8 3 5 4 Put in descending 20x + 10x − 30x + 10x order and verify number of terms. 8 5 4 3 (Both have 4 terms.) 20x − 30x + 10x + 10x
    • 22. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 )
    • 23. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 ) Distribute the monomial.
    • 24. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 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 )
    • 25. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 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.
    • 26. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 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. 2 6 4 5 3 7 2 5 6 13 4x w − 4x w + 24x w − 4x w + 12x w Verify answer has 5 terms like original parenthesis.
    • 27. Try this one... Multiply: ( 2 3x 2x − 5x + 7 )
    • 28. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) Distribute the monomial.
    • 29. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) Distribute the monomial. ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2
    • 30. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2 Multiply each term.
    • 31. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2 Multiply each term. 3 2 6x − 15x + 21x
    • 32. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b2 3 5 )
    • 33. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 ) Distribute the monomial.
    • 34. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 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
    • 35. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 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.
    • 36. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 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. 5 2 4 5 2 7 −2a b − 6a b + 8a b
    • 37. Great job working all those problems! Proceed to Part 2.