Answer:
we can conclude that:
[tex]3x^3\:-\:12xy^2=3x\left(x+2y\right)\left(x-2y\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]3x^3-12xy^2[/tex]
Let us factorize the expression
[tex]3x^3-12xy^2[/tex]
Apply the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]3x^3\:-\:12xy^2=3xx^2-12xy^2[/tex]
Rewrite 12 as 4 · 3
[tex]=3xx^2-4\cdot \:3xy^2[/tex]
Factor out the common term 3x
[tex]=3x\left(x^2-4y^2\right)[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]=3x\left(x+2y\right)\left(x-2y\right)[/tex]
Therefore, we can conclude that:
[tex]3x^3\:-\:12xy^2=3x\left(x+2y\right)\left(x-2y\right)[/tex]
