Simplify the expression.

1. (–3x3)(5x)

ANSWER –15x4

ANSWER –9x

2. 9x – 18x

3. 10y2 + 7y – 8y2 – 1

ANSWER 2y2 + 7y – 1

Check your HW 5.2

Monomial: 1 term

2x

Binomial: 2 terms xx 32

Trinomial: 3 terms 232 xx

These are all polynomials

Adding Polynomials: Combine the like terms

Like Terms – Terms that have the same variables with the same exponents on them

Combining Like Terms: Add the coefficients of each all like terms

Ex. 3x + (-5x) = [3 + (-5)]x = -2x

Add & Subtract PolynomialsAdd & Subtract Polynomials

Example:63 and 984 :Add 22 x-xxx

Rewrite )63()98(4 22 x-xxx

Combine Like Terms

23x x11 3

69384 22 xxxx

EXAMPLE 1

(3y3 – 2y2 – 7y) + (–4y2 + 2y – 5)

3y3 – 2y2 – 4y2 – 7y + 2y – 5

3y3 – 6y2 – 5y – 5

2. Add 3y3 – 2y2 – 7y and –4y2 + 2y – 5

Gather like terms

Combine like terms

EXAMPLE 2

(5z2 – z + 3) – (4z2 + 9z – 12

5z2 – 4z2 – z – 9z + 3 + 12

z2 – 10z + 15

4. Subtract 4z2 + 9z – 12 from from

5z2 – z + 3 – 4z2 – 9z + 12

Remember to distribute the – through the ( )

Gather like terms

Combine like terms

5z2 – z + 3

GUIDED PRACTICE for Examples 1 and 2

Find the sum

5. (t2 – 6t + 2) + (5t2 – t – 8)

6t2 – 7t – 6

t2 + 5t2 – 6t – t + 2 – 8

GUIDED PRACTICE for Examples 1 and 2

6. (8d – 3 + 9d3) – (d3 – 13d2 – 4)

8d3 + 13d2 + 8d + 1

Find the difference

8d – 3 + 9d3 – d3 + 13d2 + 4

9d3 – d3 + 13d2 + 8d – 3 + 4

There are three techniques you can use for multiplying polynomials.

It’s all about how you write it…

1) Distributive Property-arrow multiplication

2) FOIL – also arrow multiplication!

3) Box Method

I use arrow multiplication most often, you may use the method you like best.

Remember, FOIL reminds you to multiply the:

First terms

Outer terms

Inner terms

Last terms

The FOIL method is ONLY used when you multiply 2 binomials. It is an

acronym and tells you which terms to multiply.

Use the FOIL method to multiply the following binomials:

(y + 3)(y + 7).

(y + 3)(y + 7). F tells you to multiply the FIRST

terms of each binomial.

y2

(y + 3)(y + 7). O tells you to multiply the OUTER

terms of each binomial.

y2 + 7y

(y + 3)(y + 7). I tells you to multiply the INNER

terms of each binomial.

y2 + 7y + 3y

(y + 3)(y + 7). L tells you to multiply the LAST

terms of each binomial.y2 + 7y + 3y + 21

Combine like terms.

y2 + 10y + 21

Multiply (2x - 5)(x2 - 5x + 4)You cannot use FOIL because they are not BOTH binomials. You must use the

distributive property.

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

2x3 - 10x2 + 8x - 5x2 + 25x - 20

Group and combine like terms.

2x3 - 10x2 - 5x2 + 8x + 25x - 20

2x3 - 15x2 + 33x - 20

x2 -5x +4

2x

-5

Multiply (2x - 5)(x2 - 5x + 4) You cannot use FOIL because they are not BOTH

binomials. You must use the distributive property or box method.

2x3

-5x2

-10x2

+25x

+8x

-20

Almost done!Go to

the next slide!

x2 -5x +4

2x

-5

Multiply (2x - 5)(x2 - 5x + 4) Combine like terms!

2x3

-5x2

-10x2

+25x

+8x

-20

2x3 – 15x2 + 33x - 20

Multiply

Multiply 2 binomials

Combine like terms

Multiply the third binomial

Combine like terms

Follow the pattern

Simplify

ClassworkFinish 5.3

Homework AssignmentTextbook

Page 352 Quiz 1- 16