Question

8a3+27b3+36a2b+54ab2 factorise

Answer 1

8a³+27b³+36a²b+54ab²

=(2a)³+(3 b)³+3.4a².3+3.2a.9b²

=(2a+3b)³..

This equation follows ( a+ b)³ =a³ + b³ + 3a²b + 3ab². formula.

Ans:- (2a+3b)³

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Answer 2

$8a^{3}+27b^{3}+36a^{2}b+54ab^{2}=(2a+3b)^{3}$ or, $(2a+3b)(2a+3b)(2a+3b)$

Concept to be used:

Before we solve the problem, we must know the algebraic identity that has the power $3$, that is,

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

If we can arrange any expression similar to the right hand side, then the left hand side can be written similarly.

Step-by-step explanation:

Now, $8a^{3}+27b^{3}+36a^{2}b+54ab^{2}$

$=8a^{3}+36a^{2}b+54ab^{2}+27b^{3}$

• Here we have just rearranged the terms.

$=(2a)^{3}+3(2a)^{2}(3b)+3(2a)(3b)^{2}+(3b)^{3}$

• Here, we have written the expression into the form of $a^{3}+3a^{2}b+3ab^{2}+b^{3}$

$=(2a+3b)^{3}$

This is the required simplification and this can also be written as

$(2a+3b)(2a+3b)(2a+3b)$

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