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Multiplying a Polynomial by a Monomial

Multiplying a Polynomial by a Monomial. Lesson 7-6: Multiplying a Polynomial by a Monomial SOL A.2b. Objectives. Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials. Multiply a Polynomial by a Monomial. -3x 2 (7x 2 – x + 4)

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Multiplying a Polynomial by a Monomial

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  1. Multiplying a Polynomial by a Monomial Lesson 7-6: Multiplying a Polynomial by a Monomial SOL A.2b

  2. Objectives Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials.

  3. Multiply a Polynomial by a Monomial -3x2(7x2 – x + 4) = -3x2(7x2 + (-x) + 4) = -3x2(7x2) + (-3x2)(-x) + (-3x2)(4) = -21x4 + 3x3 + (-12x2) = -21x4 + 3x3 – 12x2 5a2(-4a2 + 2a – 7) = 5a2[-4a2 + 2a + (-7)] = 5a2(-4a2) + 5a2(2a) + 5a2(-7) = -20a4 + 10a3 + (-35a2) = -20a4 + 10a3 – 35a2

  4. Practice Time! Work this problem on your own. -6d3(3d4 – 2d3 – d + 9) = -6d3(3d4 + (-2d3) + (-d) + 9) = -6d3(3d4) + (-6d3)(-2d3) + (-6d3)(-d) + (-6d3)(9) = -18d7 + 12d6 + 6d4 + (-54d3) = -18d7 + 12d6 + 6d4 – 54d3

  5. Simplify Expressions 2p(-4p2 + 5p) – 5(2p2 +20) = 2p(-4p2 + 5p) + (-5)(2p2 + 20) = 2p(-4p2) + 2p(5p) + (-5)(2p2) + (-5)(20) = -8p3 + 10p2 + (-10p2) + (-100) = -8p3 + [10p2 + (-10p2)] + (-100) = -8p3 + (-100) = -8p3 - 100

  6. Simplify Expressions 3(5x2 + 2x – 4) – x(7x2 + 2x – 3) = 3[5x2 + 2x + (-4)] + (-x)[7x2 + 2x + (-3)] = 3(5x2) + 3(2x) + 3(-4) + (-x)(7x2) + (-x)(2x) + (-x)(-3) = 15x2 + 6x + (-12) + (-7x3) + (-2x2) + 3x = (-7x3) + [15x2 + (-2x2)] + [6x + 3x] + (-12) = -7x3 + 13x2 + 9x + (-12) = -7x3 + 13x2 + 9x – 12

  7. Practice Time! Work this problem on your own. 15t(10y3t5 + 5y2t) – 2y(yt2 + 4y2) = 15t(10y3t5 + 5y2t) + (-2y)(yt2 + 4y2) = 15t(10y3t5) + 15t(5y2t) + (-2y)(yt2) + (-2y)(4y2) = 150y3t6 + 75y2t2 + (-2y2t2) + (-8y3) = 150y3t6 + [75y2t2 +(-2y2t2)] + (-8y3) = 150y3t6 + 73y2t2 + (-8y3) = 150y3t6 + 73y2t2 – 8y3

  8. Solve Equations 2a(5a – 2) + 3a(2a + 6) + 8 = a(4a + 1) + 2a(6a – 4) + 50 2a[5a + (-2)] + 3a(2a + 6) + 8 = a(4a + 1) + 2a[6a + (-4)] + 50 10a2 + (-4a) + 6a2 + 18a + 8 = 4a2 + a + 12a2 + (-8a) + 50 [10a2 + 6a2] + [-4a + 18a] + 8 = [4a2 + 12a2] + [a + (-8a)] + 50 16a2 + 14a + 8 = 16a2 + (-7a) + 50 14a + 8 = (-7a) + 50 *Subtract 16a2 from each side. 21a + 8 = 50 *Add 7a to each side. 21a = 42 *Subtract 8 from each side. a = 2 *Divide each side by 21. Check your work! 2(2)[5(2) – 2] + 3(2)[2(2) + 6] + 8 = 2[4(2) + 1] + 2(2)[6(2) – 4] + 50 4(8) + 6(10) + 8 = 2(9) + 4(8) + 50 32 + 60 + 8 = 18 + 32 + 50 100 = 100

  9. Solve Equations d(d + 3) – d(d – 4) = 9d – 16 d(d + 3) + (-d)[d + (-4)] = 9d + (-16) d(d) + d(3) + (-d)(d) + (-d)(-4) = 9d + (-16) d2 + 3d + (-d2) + 4d = 9d + (-16) [d2 + (-d2)] + [3d +4d] = 9d + (-16) 7d = 9d + (-16) -2d = (-16) *Subtract 9d from each side. d = 8 *Divide each side by (-2). Check your work! 8(11) + (-8)(4) = 9(8) + (-16) 88 + (-32) = 72 + (-16) 56 = 56

  10. Practice Time! Work problems 1 – 17 odd on page 441 on your own.

  11. Homework Page 442 (19 – 43 odd).

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