How do you factor $8 x^{3} + 27$ $8x^3+27$ ?

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How do you factor $8 x^{3} + 27$ $8x^3+27$ ?

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Answer 1 · 2018-03-07T09:27:42

You can't factorize it as:
$8 x^{3} = 2 \times 2 \times 2 \times x \times x \times x$ $8x^3=2xx2xx2xx x xx x xx x$
And
$27 = 3 \times 3 \times 3$ $27=3xx3xx3$
Nothing is common....
$1 (8 x^{3} + 27)$ $1(8x^3+27)$ can be written

Answer 2 · 2018-04-07T08:58:16

$\Rightarrow [4 x^{2} - 6 x + 9] [2 x + 3]$ $color(magenta)(=>[4x^2-6x+9][2x+3]$

Explanation:

$8 x^{3} + 27$ $8x^3+27$

$\Rightarrow {(2 x)}^{3} + 3^{3}$ $=>(2x)^3+3^3$

Using the identity: $a^{3} + b^{3} = (a^{2} - a b + b^{2}) (a + b)$ $color(red)(a^3+b^3=(a^2-ab+b^2)(a+b)$

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

$\Rightarrow [{(2 x)}^{2} - (2 x \times 3) + 3^{2}] [2 x + 3]$ $=>[(2x)^2-(2x xx3)+3^2][2x+3]$

$\Rightarrow [4 x^{2} - 6 x + 9] [2 x + 3]$ $color(magenta)(=>[4x^2-6x+9][2x+3]$

~Hope this helps! :)

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