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

3.4

3.4Multiplying PolynomialsMultiplying MonomialsTo 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 CoefficientsAdd the Exponents of the like variables

Try a few4y5 6y3

- 5p3 6p

- 9g7 7g2

- 3x3 4x -2x2Try a few4y5 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 PowerTo 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 variables exponent by that power.Examples:

ORORTrying Another ExampleMultiplying a polynomial by a monomialTo 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)

2x(3x2 + 4x + 3)-3x2(4x2 + 5x 6)Multiplying PolynomialsCombine each term in the second polynomial by each term in the first polynomial

Combine like terms(x + 5)(x +1)(x + 4)(2x2 + 5x - 3)FOILF FirstO Outside(x + 3)(x + 2)I InsideL Last

ConjugatesConjugates 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 - 72Challenge Problems

(t + 3)(4t -1)

(n 6)(7n 3)

(y + 8)(y 8)

(x + 4)(2x2 + 5x 3)

3x2(2x 3)(x + 4)4t2 + 11t 37n2 45n +18y2 642x3 + 13x2 + 17x 126x4 + 15x3 36x2 21Homework:3.1 ODD3.2 ODD3.3 EOO3.4 EOO3.5 EOO3.6 EOO3.7 ODD