Question

factorise 8a3 + undedroot 27b3

Answer 1

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Answer 2

Answer: Our factorized form is $(2a+\sqrt{3}b)(a^2+3b^2-2\sqrt{3}ab)$

Step-by-step explanation:

Since we have given that

$8a^3+\sqrt{27}b^3$

We need to factorise the above expression:

$8a^3+\sqrt{27}b^3\\\\(2a)^3+(\sqrt{3}b)^3$

As we know the "Cubic identity":

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

So, Substitute the value of

$a = 2a\\ b=\sqrt{3}b$

So, our equation becomes,

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

Hence, our factorized form is $(2a+\sqrt{3}b)(a^2+3b^2-2\sqrt{3}ab)$