Multiplying Polynomials

Definitions

100

What are like terms?

Like-terms are two or more terms that have the same variable and exponent and can be combined through addition or subtraction. 

200

What is an exponent? 

The small number on top of a variable or number that shows how many times a term will be multiplied by itself  

300

What is a coefficient?

A coefficient is the number in front of the variable that is multiplied by the variable

400

What is a monomial?

A monomial is an algebraic expression made up of one term

500

What is a polynomial? 

A polynomial is an algebraic expression made up of multiple monomials combined using an operation such as addition or subtraction

Multiple Variables

100

2x²y²*x²y²

2x⁴y⁴

200

3x³y(2xy²)

6x⁴y³

300

6zyx(2y²x)

12zy³x²

400

5xy(2z+5xy)

10xyz + 25x²y²

500

3m²n(2m³n + ny)

6m⁵n² + 3m²n²y

Polynomials

100

3x(4x+2)

12x²+6x

200

(x-2)(5x-1)

5x²-11x+2

300

3y(y²-2y-3)

3y³-6y²-9y

400

(3p-2)(p²-6p+4)

3p³-20p²+24p-8

500

(m²-3m+2)(3m²-m+9)

3m⁴-10m³+18m²-29m+18

MORE Polynomials

100

2y(y-4)

2y²-8y

200

(m-4)(4m-2)

4m²-18m+8

300

2x(x²+x-6)

2x³+2x²-12x

400

(4y²-5)(2y²-y-5)

8y⁴-4y³-30y²+5y+25

500

(3x³-2x²-5x)(x²+6x-2)

3x⁵+16x⁴-33x³-26x²+10x

Throwback!

100

Solve for x:

2x - 5 = 15

x=10

200

Find the next term in the arithmetic sequence: 2, 8, 14...

20

300

Find the next term in the geometric sequence: 2, 6, 18...

54

400

Solve the inequality: 

4 - 3x > 16

x < -4

500

Solve the inequality:

1/2 (4y-6)<y+6

y<9