Question

Factorise 3x^3 - 12xy^2​

Answer 1

we can conclude that:

`3x^3\:-\:12xy^2=3x\left(x+2y\right)\left(x-2y\right)`

Explanation:

Given the expression

`3x^3-12xy^2`

Let us factorize the expression

`3x^3-12xy^2`

Apply the exponent rule:
`a^(b+c)=a^ba^c`

`3x^3\:-\:12xy^2=3xx^2-12xy^2`

Rewrite 12 as 4 · 3

`=3xx^2-4\cdot \:3xy^2`

Factor out the common term 3x

`=3x\left(x^2-4y^2\right)`

`\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)`

`=3x\left(x+2y\right)\left(x-2y\right)`

Therefore, we can conclude that:

`3x^3\:-\:12xy^2=3x\left(x+2y\right)\left(x-2y\right)`