Factoring

Expanding

100

(x + 3) (x +4) 

x^2 + 7x + 12

200

(3x + 1)(2x + 7)

6x^2 +23x +7

300

3(2x-1)(2x+5) 

12x^2 +24x - 15

400

4(x-2)(x-6) +3(x+3)(3x - 2)

13x^2 - 11x + 30

500

2(3y +2)(y-1) - (y-2)(2y+1)

4y² +3y - 2

Common Factoring

100

-5x + 20

-5 (x-4)

200

12x²y² - 24x

12x (xy² - 2)

300

8x³ - 6x²y² + 4x²y

2x² (4x - 3y² + 2y)

400

25k⁶ + 15k⁴ +5k²

(5k²) 5k⁴ + 3k² +1

500

2x(x-3) -5(x-3) 

(x-3)(2x-5)

Group Factoring

100

ax + ay + 2x + 2y

(x+y)(a+2)

200

ay² + 3ay + 4y + 12

(y+3)(ay+4) 

300

9x² - 6x + 6x - 4

(3x-2)(3x+2)

400

6x² + 9x - 2x - 3

(2x+3)(3x-1) 

500

4x² + 6xy + 12y + 8x

2(2x+3y)(x+2)

Factoring Trinomials

100

d² - 12d + 35

(d-7) (d-5) 

200

3x² - 12x - 36

3(x-6) (x+2)

300

6x² - 42x + 72

6 (x-4)(x-3)

400

6x² - 5xy - 4y²

(3x - 4y)(2x+y) 

500

x⁴ - 7x² - 18

(x² + 2) (x² - 9) 

(x² +2) (x - 3) (x+3) 

Special Products

100

x² - 25

(x -5)(x+5)

200

y² - 196

(y - 14)(y+14)

300

16k² - 49

(4k - 7)(4k +7)

400

4k² - 20k +25

(2k-5)²

500

16x² - 12xy - 12xy + 9y²

(4x - 3y)²