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Factorise 3x^3 - 12xy^2​

1 Answer

9 votes

Answer:

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)

User Manish Goyal
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