Factorise: 8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2} | vedclass

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Question

(A) The given expression is $8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$.We can rewrite the expression as $(2 a)^{3}+(b)^{3}+3(2 a)^{2}(b)+3(2 a)(b)^{2}$.This

Vedclass · Accepted Answer

$(2a+b)^3$

Vedclass · Answer

(A) The given expression is $8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$.We can rewrite the expression as $(2 a)^{3}+(b)^{3}+3(2 a)^{2}(b)+3(2 a)(b)^{2}$.This is in the form of the algebraic identity $(x+y)^{3} = x^{3}+y^{3}+3 x^{2} y+3 x y^{2}$,where $x = 2a$ and $y = b$.Therefore,the expression simplifies to $(2 a+b)^{3}$.Thus,the factorised form is $(2 a+b)(2 a+b)(2 a+b)$.

Factorise: $8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$

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