34
POLYNOMIALS

POLYNOMIALS. MULTIPLYING POLYNOMIALS REVIEW Polynomials:

Embed Size (px)

Citation preview

POLYNOMIALS

MULTIPLYING POLYNOMIALS

REVIEW

Polynomials:

To multiply polynomials:

1) Multiply each term in one polynomial by each term in another polynomial

2) Simplify as needed (collect like terms)

1 TERM X 1 TERM

Multiplying a monomial by another monomial:

1) Multiply the constants together

2) Multiply the variables together

3) Combine the result

EXAMPLE:

(2y)(3y)

1) (2)(3) = 6

2) (y)(y) = ?

NOTE: We use brackets to represent multiplication so that we don’t

confuse it with our variable ‘x’

1) Multiply the constants together2) Multiply the variables together3) Combine the result

MULTIPLYING VARIABLES WITH EXPONENTSWe know y² = yy

We know y³ = yyy

So (y²)(y³) = yyyyy = y⁵

However, instead of breaking it down into y’s, we can just add the exponents:

So (y²)(y³) = y²⁺³ = y⁵

Let’s look back at our example

EXAMPLE:

(2y)(3y)

1) (2)(3) = 6

2) (y)(y) = ?

(y)(y) = y¹⁺¹ = y²

3) (2y)(3y) = 6y²

1) Multiply the constants together2) Multiply the variables together3) Combine the result

EXAMPLE:

(4z²)(1/2z³)

1) Multiply the constants together2) Multiply the variables together3) Combine the result

EXAMPLE:

(-6x⁴y)(2xz³)

1) Multiply the constants together2) Multiply the variables together3) Combine the result

EXAMPLE:

(-3ab⁴c²)(-4a²bc³)

1) Multiply the constants together2) Multiply the variables together3) Combine the result

1 TERM X 2 TERMS

We call this the Distributive Property

Multiply the single term by each of the two terms

LET’S CHECK IF IT WORKS

EXAMPLE:• 2(x+7)

EXAMPLE:• 2x(x³+3y)

EXAMPLE:• (b³-2abc) 3a²b

1 TERM X 3+ TERMS

This is still the distributive property

We will multiply the single term by each of the other terms

a(b + c + d + …) = ab + ac + ad + …

EXAMPLE

4y²(3x⁵ - xy³ - y²z)

EXAMPLE

(5a⁵ - b³ + 4a²b) 2b²

2 TERMS X 2 TERMS

(a + b)(c + d) = ac + ad + bc + bd

This process is called FOILING

First

Outside

Inside

Last

STEP BY STEP

EXAMPLE:

EXAMPLE:

(x – 2)(x+6)

EXAMPLE:

(4x – 2)(3x+6)

EXAMPLE:

(xy – 2y)(3x²+6)

EXAMPLE:

(3x³y + 2y³)(x² - 4xy)

2 TERMS X 3+ TERMS

We can extend the FOIL method to any polynomials being multiplied together

(a + b)(c + d + e) = ac + ad + ae + bc + bd + be

Multiply ‘a’ with all the terms in the second polynomial

Multiply ‘b’ with all the terms in the second polynomial

ANY TERMS X ANY TERMS

This would be true for any number of terms

(a + b + c)(d + e + f) = ad + ae + af + bd + be + bf + cd + ce + cf

EXAMPLE:

(x + 2y)(3x − 4y + 5)

EXAMPLE:

(x - 4)(3x - y + 3)

EXAMPLE:

What is the product of  (2y - 1), (2y + 1) and (4y2 + 1)?

YOUR TURN!!