Multiplying Polynomials

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

 Multiply the Coefficients  Add the Exponents of the like variables

 4y 5 × 6y 3  - 5p 3 × 6p  - 9g 7 × 7g 2  - 3x 3 × 4x × -2x 2

 4y 5 × 6y 3 (4)(6)(y 5+3 ) 24y 8  - 5p 3 × 6p (-5)(6)(p 3+1 ) -30p 4  - 9g 7 × 7g 2 (-9)(7)(g 7+2 ) -63g 9  - 3x 3 × 4x × -2x 2 (-3)(4)(-2)(x ) 24x 6

 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.

OR Trying Another Example

 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)

 Combine each term in the second polynomial by each term in the first polynomial  Combine like terms

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

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

(x + 7)(x – 7) = x

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