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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 Multiplying Polynomials
Multiplying Monomials To multiply exponential forms that have the same base, we can add the exponents and keep the same base.
To Multiply Monomials: Multiply the Coefficients Add the Exponents of the like variables
Try a few • 4y5 × 6y3 • - 5p3 × 6p • - 9g7 × 7g2 • - 3x3 × 4x × -2x2
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
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.
Examples: OR Trying Another Example OR
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)
Multiplying Polynomials Combine each term in the second polynomial by each term in the first polynomial Combine like terms
FOIL F First O Outside (x + 3)(x + 2) I Inside L Last
Conjugates Conjugates are binomials that differ only in the sign that separating the terms. The conjugate of (x + 7) = (x – 7)
The product of conjugates is a difference of two squares. (x + 7)(x – 7) = x2 - 72
(t + 3)(4t -1) (n – 6)(7n – 3) (y + 8)(y – 8) (x + 4)(2x2 + 5x – 3) 3x2(2x – 3)(x + 4)