Factoring the Factoring the Sum or the Sum or the Difference of Difference of Two Cubes.Two Cubes.Subtitle: Know the

Subtitle: Know the

CARD!!!CARD!!!

Multiple the Multiple the following:following:

32x

3

3 2

2 2 2 2

6 12 8

x x x x

x x x

Special Factor Special Factor PatternsPatterns

3 3 2 2

3 3 2 2

a b a b a ab b

a b a b a ab b

S

S

O

O

AP

AP

ExamplesExamples

3 3 2 2

3 8

a b a b a ab b

x

S O A

P

3 3 2 2

38 1

a b a b a ab b

x

S O A

P

ExamplesExamples

3 3 2 2

3 28 2 2 4

a b a b a ab b

x x x x

S O A

P

3 3 2 2

3 28 1 2 1 4 2 1

a b a b a ab b

x x x x

S O A

P

Example 1 from Example 1 from Notes:Notes:

3 125z

3 35z S O A

P327 64x 3 33 4x

S O A

P

3 125z

25 5 25z z z

3 35z S O A

P327 64x 3 33 4x

23 4 9 12 16x x x S O A

P

More More Examples:Examples:

6 729a

2 4 29 9 81a a a

32 39a S O A

P

4 23 3 9 81a a a a

Difference of Two Squares

Completely Factored

More More Examples:Examples:

31000 1x 3 310 1x

210 1 100 10 1x x x S O AP

481 192y y 33 27 64y y

23 3 4 9 12 16y y y y Completely Factored

S O AP

Your Turn38 64x 38 8x

28 2 2 4x x x 5 25 625m m 2 35 125m m

2 25 5 5 25m m m m

Factoring By Factoring By GroupingGrouping

Example 2 from Example 2 from Notes:Notes:

3 22 9 18x x x

2 2 9 2x x x

2 9 2x x

3 3 2x x x

More More Examples:Examples:3 3 3 36 6am an m n

Completely Factored

3 3 3 36a m n m n

3 36a m n Difference of Two Cubes

2 26a m n m mn n

Example 3 from Notes:Example 3 from Notes:

416 256x 416 16x

2 216 4 4x x

216 2 2 4x x x

Example 3 from Notes:Example 3 from Notes:

7 5 33 15 18y y y

3 4 23 5 6y y y

3 2 23 3 2y y y

Your Turn

3 22 25 50x x x

2 2 25 2x x x

2 25 2x x

5 5 2x x x

Your Turn

4 214 45x x

2 29 5x x

23 3 5x x x

SolvingSolvingPolynomialPolynomial

Equations by Equations by FactoringFactoring

Example 4 from Notes:Example 4 from Notes:

4 29 10x x 4 210 9 0x x

2 29 1 0x x 3 3 1 1 0x x x x

3, 3, 1, 1x x x x 3, 1x

Your Turn5 32 24 14x x x

5 32 14 24 0x x x 4 22 7 12 0x x x

2 22 4 3 0x x x

22 2 2 3 0x x x x

0, 2, 2, 3x x x x