BASIC ALGEBRA

Warm Up Factors

100

3x²−5x−2

(3x+1)(x−2)

200

9y²−25

(3y−5)(3y+5)

300

 9y²−12y+4 

(3y−2)²

400

27y³+1

(3y+1)(9y2−3y+1)

500

16x²−y²

Difference of squares:

=(4x−y)(4x+y)

Square It Out

100

4x²+12x+9

(2x+3)²

200

4a²−b²

(2a−b)(2a+b)

300

x²+12x+36

(x+6)²

400

6x²+12x

6x(x+2)

500

x³−125

Difference of cubes:

=x³−5³

=(x−5)(x²+5x+25) 

Spot the Difference

100

5x²−20x+15

5(x−1)(x−3)

200

x²−36

(x−6)(x+6)

300

8x²−18

Factor out the GCF (2):

=2(4x²−9)

Difference of squares:

=2(2x−3)(2x+3)

400

15a³−30a²

15a²(a−2)

500

x²−81

Difference of squares:

=(x−9)(x+9)

Common Factor Zone

100

x²+7x+10

Find two numbers that multiply to 10 and add to 7.
= 5 and 2

= x²+7x+10

= (x+5)(x+2)

200

5x²−20

First, factor out the GCF (5):

=5(x²−4)

Then factor the difference of squares:

=5(x−2)(x+2)

300

3x²+8x+4

Multiply A x C = 3 x 4 = 12

Find two numbers that multiply to 12 and add to 8 → 6 and 2

= 3x²+6x+2x+4

Group terms:

=3x(x+2)+2(x+2) 

=(3x + 2)(x + 2)

400

x³+8

This is a sum of cubes:

x³+2³

Formula:

=a³+b³=(a+b)(a²−ab+b²)

=(x + 2)(x² - 2x + 4)

500

4x²−49

Difference of squares:

=(2x−7)(2x+7)

Cube Crushers

100

x²+2x−15

Numbers that multiply to −15 and add to 2 to 5 and −3

=(x+5)(x−3)

200

x²−49

Difference of squares:

=(x−7)(x+7)

300

x²−x−12

Find two numbers that multiply to −12 and add to −1.
= −4 and 3

=(x−4)(x+3)

400

x³−64

Difference of cubes:

=x³−4³

Formula:

=a³−b³=(a−b)(a²+ab+b²)

= (x−4)(x²+4x+16) 

500

4x²−25y²

This is a difference of squares:

4x²=(2x)² and 25y²= (5y)²

= 4x² - 25y² 

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