How do you factor $8 x^{3} - 36 x^{2} + 54 x - 27$ $8x^3 - 36x^2 + 54x - 27$ ?

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How do you factor $8 x^{3} - 36 x^{2} + 54 x - 27$ $8x^3 - 36x^2 + 54x - 27$ ?

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Answer 1 · 2015-09-28T06:28:22

Notice that $8 x^{3} = {(2 x)}^{3}$ $8x^3 = (2x)^3$ and $- 27 = {(- 3)}^{3}$ $-27 = (-3)^3$ , so is the answer ${(2 x - 3)}^{3}$ $(2x-3)^3$ ?

Multiply out ${(2 x - 3)}^{3}$ $(2x-3)^3$ and find that it is.

$8 x^{3} - 36 x^{2} + 54 x - 27 = {(2 x - 3)}^{3}$ $8x^3-36x^2+54x-27 = (2x-3)^3$

Explanation:

In general, ${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

Putting $a = 2 x$ $a=2x$ and $b = - 3$ $b=-3$ we find:

${(2 x - 3)}^{3} = {(2 x)}^{3} + 3 {(2 x)}^{2} (- 3) + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$ $(2x-3)^3 = (2x)^3 + 3(2x)^2(-3) + 3(2x)(-3)^2 + (-3)^3$

$= 8 x^{3} - 36 x^{2} + 54 x - 27$ $=8x^3-36x^2+54x-27$

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How do you factor $8 x^{3} - 36 x^{2} + 54 x - 27$ $8x^3 - 36x^2 + 54x - 27$ ?

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