Factor the expression. c^3-512?

a]-{c-8}{c^2+8c+64}


b]{c-8}{c^2+8c=64}


c]{c+8}{c^2+8c=64}


d]{c-8{c^2-8c-64}

Factor the expression. c^3-512?
(c-8)(c^2+8c+64) is the answer


C is the answer if you replace the = sign by + sign.
Reply:the best answer is B. when you are factoring an equation thats to the third power theres a trick to it. when its c^3-512 it would be (c-8)(c^2+8c=64)=(c-8)(c^2+8c-64) what ever the symbol is in the first equation would start of in the next on. it it were positibe it would be (c+8)(c^2-8c=64)=(c+8)(c^2-8c-64)





its difference of perfect cubes.
Reply:difference of cubes:





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





if you get stuck with this in a test, i suggest you work backwards and apply the distributive property with each answer.
Reply:This is a difference of perfect cubes since 512 = 8^3. In general, the difference of perfect cubes can be factored as follows:





Consider (c-a)^3 = (c-a)*(c-a)^2 = (c-a)*(c^2-2ac+a^2) = c^3-2ac^2+ca^2-ac^2+2a^2c-a^3 = c^3-3ac^2+3a^2c-a^3. Therefore, upon rearranging terms, c^3-a^3 = (c-a)^3+3ac^2-3a^2c = (c-a)^3 +3ac(c-a) = (c-a)((c-a)^2+3ac) = (c-a)(c^2-2ac+a^2+3ac) = (c-a)*(c^2+ac+a^2) (whew)





In our case, a = 8 and therefore c^3-512 = (c-8)(c^2+8c+64), which I think is answer (b), other than the typo (= instead of +).





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