Polynomials

Add/Subtract

100

Simplify the following:

5x-4y+6+2y+x+10

6x-2y+16

200

Simplify the following:

6ab³ - ab+6a⁴b+7a⁴b - 3ab

6ab³ + 13a⁴b - 4ab

300

Simplify the following

-xy² - 5y² + 6xy² + 8x² + 3x²y - 5y² - 3x²y

=5xy² - 10y² +8x²

400

Simplify

3(x³+1) + 2(x²-5)

=5x³ +2x² - 7

500

Simplify:

(4ab + 3a - b) - (2ab +4a - 7b - 4)

=2ab - a +6b + 4

Multiply

100

(x-4)(x+3)

=x²-x-12

200

(x+12)(x+11)

=x²+23x+132

300

(2x-5)(2x+5)

=4x²-25

400

(5x-12)(4x+9)

=20x²-3x-108

500

(x-2)(x²-10x+3)

=x³ - 12x² + 23x - 6

Something Common

100

Factor the following: 

4x - 6xy +12y - 12

= 2(2x - 3xy + 6y - 6)

200

Factor: 

3a⁴b²-10a²b+16a³b⁵

= a²b(3a²b - 10 + 16ab⁴)

300

Factor:

24f⁵ - 80f³g³ - 16f²g + 40f⁶

=8f²(3f³ - 10fg³ - 2g + 5f⁴)

400

Factor:

4x(x-3)+9(x-3)- 7y(x-3)

=(x-3)(4x+9-7y)

500

Factor

54 - 90y + 3xy - 303x

=3(18-30y+xy - 101x)

Factor Trinomials

100

Factor:

x² - 3x + 2

= (x-1)(x-2)

200

Factor: 

x² + 13x + 36

=(x+9)(x+4)

300

Factor: 

x² -15x + 44

= (x-11)(x-4)

400

Factor: 

2x² - x -10

= (2x-5)(x+2)

500

Factor: 

4x² - 24x + 27

= (2x-9)(2x-3)

Special Polynomials

100

Factor:

a² - 9

= (a-3)(a-3)

200

Factor: 

25b² - 81c²

= (5b-9c)(5b+9c)

300

Factor:

x² + 14x +49

= (x + 7)²

400

Factor: 

36m² - 4n²

= 4(3-n)(3+n)

500

25x² - 30x +9

=(5x-3)²