Factoring Polynomials

Difference of Squares

100

Factor the following:

3n²-75

Answer:

3(n-5)(n+5)

300

Factor the following:

125m²-20n²

5(25m²-4n²)=

5(5m-2n)(5m+2n)

500

Factor the following:

64x⁶-y⁸

(6x³-y⁴)(6x³+y⁴)

Sum of Cubes

100

Factor the following:

8a³+125

(2a+5)(4a²-10a+25)

300

Factor the following:

216x³+64y³

(6x)³+(4y)³

(6x+4y)(36x²-24xy+16y²)

2((3x+2y)(18x²-12xy+8y²))

500

Factor:

-8x⁴+x

x((-2x)³+(1)³)

x(-2x+1)(4x²+2x+1)

or

-x((2x)³-(1)³)

-x(2x-1)(4x²+2x+1)

Difference of Cubes

100

Factor

1-a³

(1)³-(a)³ =

(1-a)(1+a+a²)

300

Factor:

-a³-8

(-a)³-(2)³

= (-a-2)(a²-2a+4)

or

-((a)³+(2)³)

=-(a+2)(a²-2a+4)

500

Factor:

-2a³-16

2((-a)³-(2)³)

= 2(-a-2)(a²-2a+4)

or

-2((a)³-(2)³)

=-2(a+2)(a²-2a+4)