swadeshdarai14
Answered

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factorise 3x^3 - 12xy^2​

Sagot :

absor201

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]

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