How do you factor: $y = x^{3} - 27$ $y= x^3 - 27$ ?

Question

How do you factor: $y = x^{3} - 27$ $y= x^3 - 27$ ?

1 Answer

Impact of this question

2367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T19:03:02

$y = x^{3} - 27 = (x - 3) (x^{2} + 3 x + 9)$ $y=x^3-27=(x-3)(x^2+3x+9)$

Explanation:

Both $x^{3}$ $x^3$ and $27 = 3^{3}$ $27=3^3$ are perfect cubes. So it is natural to use the difference of cubes identity:

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $a^3-b^3=(a-b)(a^2+ab+b^2)$

with $a = x$ $a=x$ and $b = 3$ $b=3$ as follows:

$x^{3} - 27$ $x^3-27$

$= x^{3} - 3^{3}$ $=x^3-3^3$

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

$= (x - 3) (x^{2} + 3 x + 9)$ $=(x-3)(x^2+3x+9)$

Science

Math

Humanities

... and beyond

How do you factor: $y = x^{3} - 27$ $y= x^3 - 27$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor: y= x^3 - 27 y=x3−27y= x^3 - 27 ?

1 Answer

Explanation:

Related questions

Impact of this question

How do you factor: $y = x^{3} - 27$ $y= x^3 - 27$ ?