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