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3.4

3.4. Multiplying Polynomials. Multiplying Monomials. To multiply exponential forms that have the same base, we can add the exponents and keep the same base. In other words…. To Multiply Monomials:. Multiply the Coefficients Add the Exponents of the like variables. Try a few. 4y 5 × 6y 3

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3.4

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  1. 3.4 Multiplying Polynomials

  2. Multiplying Monomials To multiply exponential forms that have the same base, we can add the exponents and keep the same base.

  3. In other words…

  4. To Multiply Monomials: Multiply the Coefficients Add the Exponents of the like variables

  5. Try a few • 4y5 × 6y3 • - 5p3 × 6p • - 9g7 × 7g2 • - 3x3 × 4x × -2x2

  6. Try a few • 4y5 × 6y3 • (4)(6)(y5+3) • 24y8 • - 5p3 × 6p • (-5)(6)(p3+1) • -30p4 • - 9g7 × 7g2 • (-9)(7)(g7+2) • -63g9 • - 3x3 × 4x × -2x2 • (-3)(4)(-2)(x3+1+2) • 24x6

  7. Simplifying Monomials Raised to a Power • To simplify an exponential form raised to a power, we can multiply the exponents and keep the same base • Evaluate the coefficient raised to that power. • Multiply each variable’s exponent by that power.

  8. Examples: OR Trying Another Example OR

  9. Multiplying a polynomial by a monomial • To Multiply a polynomial by a monomial, use the distributive property to multiply each term in the polynomial by the monomial. • 2(3 + 4) = (2)(3) + (2)(4) • X(3 + 4) = (X)(3) + (X)(4)

  10. 2x(3x2 + 4x + 3)

  11. -3x2(4x2 + 5x – 6)

  12. Multiplying Polynomials Combine each term in the second polynomial by each term in the first polynomial Combine like terms

  13. (x + 5)(x +1)

  14. (x + 4)(2x2 + 5x - 3)

  15. FOIL F  First O Outside (x + 3)(x + 2) I  Inside L  Last

  16. Conjugates Conjugates are binomials that differ only in the sign that separating the terms. The conjugate of (x + 7) = (x – 7)

  17. The product of conjugates is a difference of two squares. (x + 7)(x – 7) = x2 - 72

  18. Challenge Problems

  19. (t + 3)(4t -1) (n – 6)(7n – 3) (y + 8)(y – 8) (x + 4)(2x2 + 5x – 3) 3x2(2x – 3)(x + 4)

  20. Homework:3.1 ODD3.2 ODD3.3 EOO3.4 EOO3.5 EOO3.6 EOO3.7 ODD

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