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Chapter Nine Section Three

Chapter Nine Section Three. Multiplying a Polynomial by a Monomial. What You’ll Learn. You’ll learn to multiply a polynomial by a monomial. Why it’s Important. Recreation You can use polynomials to solve problems involving recreation.

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Chapter Nine Section Three

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  1. Chapter Nine Section Three Multiplying a Polynomial by a Monomial

  2. What You’ll Learn You’ll learn to multiply a polynomial by a monomial.

  3. Why it’s Important Recreation You can use polynomials to solve problems involving recreation.

  4. Suppose you have a square whose length and width are x feet. If you increase the length by 3 feet, what is the area of the new figure? You can model this problem by using algebra tiles. The figures on the next slide show how to make a rectangle whose length is x + 3 feet and whose width is x feet.

  5. x + 3 ft. x 1 1 1 x2 x x x x2 x x x x x ft. The area of any rectangle is the product of its length and its width. The area can be found by adding the areas of the tiles.

  6. x + 3 ft. x 1 1 1 x2 x x x x2 x x x x x ft. Formula A = lw A = (x + 3)x or x(x + 3) A = x2+ 3x • Since the areas are equal, x(x + 3) = x2 + 3x square feet. • The example above shows how the Distributive Property can be used to multiply a polynomial by a monomial.

  7. ab ac

  8. Example One Find each product. y(y + 5) y(y + 5) = y(y) + y(5) = y2 + 5y y 5 y2 5y y

  9. Example Two Find each product. b(2b2 + 3) b(2b2 + 3)= b(2b2) + b(3) = 2b3 + 3b 2b2 +3 2b3 3b b

  10. Example Three Find each product. -2n(7 – 5n2) -2n(7 – 5n2) = -2n(7) + -2n(5n2) = -14n + 10n3 7 -5n2 -14n 10n3 -2n

  11. Example Four Find each product. 3x3(2x2 – 5x + 8) 3x3(2x2 – 5x + 8) = 3x3(2x2) + 3x3(-5x) + 3x3(8) = 6x5 – 15x4 + 24x3

  12. Your Turn Find each product. 7(2x + 5) 14x + 35

  13. Your Turn Find each product. 4x(3x2 - 7) 12x3 - 28x

  14. Your Turn Find each product. -5a(6 – 3a2) -30a + 15a3

  15. Your Turn Find each product. 2m2(5m2 – 7m + 8) 10m4 – 14m3 + 16m2

  16. Example Five Many equations contain polynomials that must be multiplied. Solve each equation. 11(y -3) + 5 = 2(y +22) 11y – 33 + 5 = 2y + 44 Distributive Property 11y – 28 = 2y + 44 Combine Like Terms -2y -2y Subtract 2y from each side 9y – 28 = 44 + 28 +28 Add 28 to each side. 9y = 72 Divide each side by 9 9 9 Y = 8

  17. Example Six Solve each equation. w(w + 12) = w(w + 14) + 12 w(w + 12) = w(w + 14) + 12 Distributive Property w2 + 12w = w2 + 14w + 12 -w2 -w2 Subtract w2 from each side 12w = 14w + 12 -14w -14w Subtract 14w to each side. -2w = 12 Divide each side by -2 -2 -2 w = -6

  18. Your Turn Solve each equation. 2(5x - 12) = 6(-2x + 3) + 2 2

  19. Your Turn Solve each equation. a(a + 2) + 3a = a(a - 3) + 8 1

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