help with factoring (sums and differences of cubes)?

Question

1. 64r^3 - 27

2. x^3 + y^3

3. 64 - c^12

4. x^3 - y^6

Thanks for the help!!

Answer 1

a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)

1.)
64r^3 - 27 = (4r - 3)(16r^2 + 12r + 9)

-------------------

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

--------------------------

3.)
64 - c^12 =
(4 - c^4)(16 + 4c^4 + c^8) =
(2 - c^2)(2 + c^2)(16 + 4c^4 + c^8) =

using www.quickmath.com this factors further to

(2 - c^2)(2 + c^2)(4 - 2c^2 + c^4)(4 + 2c^2 + c^4)

The only difference in my answer and theres is i didn't change anything around.

-----------------------------------------

4.)
x^3 - y^6 = (x - y^2)(x^2 + xy^2 + y^4)

Answer 2

These are fairly easy to memorize and summarize everything:
x³ + y³ = (x + y)(x² - xy + y²)
x³ - y³ = (x - y)(x² + xy + y²)

1) 64r³ - 27 =

(4r - 3)(16r² + 12r + 9)

Now, just follow on doing the same thing.

Answer 3

A^3 + B^3 = (A + B)(A^2 - AB + B^2)
A^3 - B^3 = (A - B)(A^2 + AB + B^2)

1. A = 4r, B = 3

2. A = x and B = y

4. A = x and B = y^2

3. (8)^2 - (c^6)^2 >>>A^2 - B^2 = (A + B)(A - B)<<<<
= (8 + c^6)(8 - c^6)
= [(2)^3 + (c^2)^3][(2)^3 - (c^2)^3]

NOW USE THE FORMULAE AND SAIL

Answer 4

In general,
x^3 - y^3 = (x-y)(x^2 + xy + y^2), and
x^3 + y^3 = (x + y)(x^2 - xy +y^2).
You can check this just by muliplying it out.

Answer 5

1. (4r-3)(16r^2+12r+9)

2. (x+y)(x^2-xy+y^2)

3. (4-c^4)(16+4c^4+c^8)

4. (x-y^2)(x^2+xy^2+y^4)