Simplifying Polynomial Expressions

Multiplying Binomials

100

3x(x+1)

 3x² + 3x

200

x²(3x+1)

3x³+x²

300

(x+1)(x-3)

 x²-2x-3

400

(2x+1)(3x²-4)

6x³+3x²-8x-4

500

(3x²+6)(2x+x²)

3x⁴+ 6x³+ 6x²+ 12x

Steps to Simplify:

100

When adding polynomials, you must combine _______   ________.

like terms

200

When adding polynomials, what happens to to the exponents?

 "keep the exponents the same"

300

When adding polynomials, what happens to the coefficients of each term?

combine like terms/add coefficients

400

When multiplying polynomials, what happens to the exponents?

add the exponents

500

When multiplying polynomials in a multiplication table, what do you do with partial products?

add up the partial products and combine like terms

Adding Polynomials

100

3y⁴ + 6y⁴

 9y⁴

200

-13a³ + 17a³

4a³

300

4n⁵ + 6n⁵ – 11x⁴

10n⁵ – 11x⁴?

400

12y² – 4x + 5x

12y² + x

500

–3x² + 10x² + 6x²

13x² 

Polynomial Vocabulary

100

The number or variable located^(here)

exponent

200

A numerical expression, variable, or symbol

polynomial

300

A polynomial with only one term

monomial

400

A polynomial with two terms

binomial

500

A polynomial with 3 terms

trinomial

Subtracting Polynomials

100

(8x - 5) + (2x - 14)

10x – 19

200

(9x - 6) – (-5x + 7)

14x – 13

300

-x² + 4x + 2 - 3x² - 5x + 9

 - 4x²  – x + 11

400

-7x² + 2x + 2 - 5x²  - 6x - 7

What is - 12x²  - 4x - 5 ?

500

6xy² + 3x - 4xy² - x² + 7x

What is 2xy² - x² + 10x ?