Factoring the Sum & Difference
of Two Cubes
p.368-371
This is a piece of cake, if you have perfect cubes.
What are perfect cubes?
This is a piece of cake, if you have perfect cubes.
What are perfect cubes?
Something times something times something.
Whe...
This is a piece of cake, if you have perfect cubes.
What are perfect cubes?
Something times something times something.
Whe...
The sum or difference of two cubes will factor into a
binomial × trinomial.

(

a + b = ( a + b ) a − ab + b
3

3

2

2

)...
Now we know how to get the signs, let’s work on
what goes inside.
Square this term to get this term.

(

a + b = ( a + b )...
Try one.

27 x −125 =
3

Make a binomial and a trinomial
with the correct signs.
Try one.

27 x −125 =
3

(

−

Cube root of 1st term

)(

+

+

)

Cube root of 2nd term
Try one.

27 x −125 = ( 3x − 5)(
3

+

+

)

Square this term to get this term.
Try one.

27 x −125 = ( 3x − 5) ( 9 x 2 +
3

+

)

Multiply 3x an 5 to get this term.
Try one.

27 x −125 = ( 3x − 5) ( 9 x + 15 x +
3

2

Square this term to get this term.

)
Try one.

(

27 x −125 = ( 3 x − 5) 9 x + 15 x + 25
3

2

)

You did it!

Don’t forget the first rule of factoring is to l...
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Factoring Cubes

  1. 1. Factoring the Sum & Difference of Two Cubes p.368-371
  2. 2. This is a piece of cake, if you have perfect cubes. What are perfect cubes?
  3. 3. This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something times something. Where the something is a factor 3 times. 8 is 2 × 2 × 2, so 8 is a perfect cube. x6 is x2 × x2 × x2 so x6 is a perfect cube. It is easy to see if a variable is a perfect cube, how?
  4. 4. This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something times something. Where the something is a factor 3 times. 8 is 2 × 2 × 2, so 8 is a perfect cube. x6 is x2 × x2 × x2 so x6 is a perfect cube. It is easy to see if a variable is a perfect cube, how? See if the exponent is divisible by 3. It’s harder for integers.
  5. 5. The sum or difference of two cubes will factor into a binomial × trinomial. ( a + b = ( a + b ) a − ab + b 3 3 2 2 ) same sign always + always opposite ( a − b = ( a − b ) a + ab + b 3 3 same sign always opposite 2 2 ) always +
  6. 6. Now we know how to get the signs, let’s work on what goes inside. Square this term to get this term. ( a + b = ( a + b ) a − ab + b 3 3 2 2 ) Cube root of 1st term Cube root of 2nd term Product of cube root of 1st term and cube root of 2nd term.
  7. 7. Try one. 27 x −125 = 3 Make a binomial and a trinomial with the correct signs.
  8. 8. Try one. 27 x −125 = 3 ( − Cube root of 1st term )( + + ) Cube root of 2nd term
  9. 9. Try one. 27 x −125 = ( 3x − 5)( 3 + + ) Square this term to get this term.
  10. 10. Try one. 27 x −125 = ( 3x − 5) ( 9 x 2 + 3 + ) Multiply 3x an 5 to get this term.
  11. 11. Try one. 27 x −125 = ( 3x − 5) ( 9 x + 15 x + 3 2 Square this term to get this term. )
  12. 12. Try one. ( 27 x −125 = ( 3 x − 5) 9 x + 15 x + 25 3 2 ) You did it! Don’t forget the first rule of factoring is to look for the greatest common factor.

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