SOLUTION: how to factor out 8x^3+64

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Question 320624: how to factor out 8x^3+64
Found 3 solutions by mananth, solver91311, nyc_function:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
8x^3+64
..
(2x)^3+(4)^3
This of the form a^3+b^3= (a+b)(a^2-ab+b^2)
(2x+4)(4x^2-8x+16)
2(x+2)*4(x^2-2x+4)
8(x+2)(x^2-2x+4)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


This is the sum of two cubes. Memorize the pattern for the sum and difference of two cubes:



Then recognize that



and



You should be able to take it from here.

John

Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
This is addition of cubes.
Use the following formula:
a^3 + b^3 = (a + b)(a^2 – ab + b^2)
Write 8 as 2^3 and 64 as 4^3 to get the same exponent of 3.
(2x)^3 + 4^3 = (2x + 4)((2x)^2 - (2x)(4) + 4^2)
(2x)^3 + 4^3 = (2x + 4)(4x^2 - 8x + 16)
So, 8x^3 + 64 in factored form looks like this: (2x + 4)(4x^2 - 8x + 16)