can someone help me with this math? (algebra 2)?

Question

ok its factoring. I was supposed to learn it in 9th grade but i was in an advanced class and skipped the class where i should have learned it. So i only know a little bit of factoring. it doesn't help that my math teacher is an idiot and just rambles on about football (he is the varsity coach) all hour.

so can someone explain to me how to factor the sum or the difference of to cubes. I dont just want an answer to the problems i want to understand how to do it.

i cant make the little threes for the cubed signs on the computer but here are some example problames.

8Xcubed - 1

Xcubed - Y cubed


thanks for the help.

Answer 1

When you have a difference of cubes:
a^3 - b^3

You can factor out an (a - b):
(a - b)(a² + ab + b²)

You can derive this, or memorize it. I always forget so either have to look it up or do synthetic division. If you multiply this out, you'll see you get back to a^3 - b^3.

Multiplying out:
(a^3 + a²b + ab² - a²b - ab² - b^3)

Cancelling terms:
a^3 - b^3

So (a - b)(a² + ab + b²) is the correct factoring.

Once you know that, you just have to figure out what are the cubes in your difference.

PROBLEM 1:
8x^3 - 1

This is the same as:
(2x)^3 - (1)^3

So a = 2x and b = 1

Plug that in to the formula above:
(2x - 1)((2x)² + (2x)(1) + (1)²)

Then simplify:
(2x - 1)(4x² + 2x + 1)

PROBLEM 2:
This is easy: a = x, b = y

(x - y)(x² + xy + y²)

Answer 2

Use ^(3) to indicate 'cubed'.
Difference of two cubes is a standard result.
X^(3) - Y^(3) = [X - Y] [ X^(2) +XY + Y^(2)], check it by distributing the right hand side square brackets.

The first part is a special case: {2X}^(3) -1^(3); you finish it.

Answer 3

Sum of cubes: A³ + B³ = (A + B)(A² − AB + B²)
Difference of cubes: A³ − B³ = (A − B)(A² + AB + B²)

8X³- 1³
= (2x)³-1³
= put (2x) where you see A & 1 where you see B
= (A + B)(A² − AB + B²)

X³ - Y ³
= put X where you see A & Y where you see B
= (A + B)(A² − AB + B²)

Answer 4

In general:
a^3 + b^3 = (a+b)(a^2-ab-b^2)
a^3 - b^3 = (a-b)(a^2+ab+b^2)

So 8x^3-1 has a = 2x and b = 1
8x^3-1 = (2x-1)(4x^2 + 2x + 1)

Straightforward

Answer 5

the formula for the cubed binomial is
x^3-y^3=(x-y)(x^2+xy+y^2)

if it was 8x^3-1... you would think of it as 2^3*x^3-1^3
so it would equal to (2x-1)(4x^2+2x+1)

Answer 6

8x^3 - 1 [ 8 = 2cube; 1cube = 1]
2^3. x^3 - 13
(2x)^3 - 1 3
This is in the form a^3 - b^3 where a = 2x, b =1
a^3 - b^3 = (a-b)(a^2+ab+b^2)
= (2x-1)(4x^2 +2x+1)



x^3-y^3= (x-y)(x^2+xy+y^2)