Factorise the following: 8a^3 - b^3 - 12a^2b | vedclass

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Question

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

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$(2a - b)^3$

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(A) The given expression is $8a^3 - b^3 - 12a^2b + 6ab^2$.We can rewrite this as $(2a)^3 - (b)^3 - 3(2a)^2(b) + 3(2a)(b)^2$.This expression is in the form of the algebraic identity $(x - y)^3 = x^3 - y^3 - 3x^2y + 3xy^2$,where $x = 2a$ and $y = b$.Therefore,$8a^3 - b^3 - 12a^2b + 6ab^2 = (2a - b)^3$.This can be written as $(2a - b)(2a - b)(2a - b)$.

Factorise the following: $8a^3 - b^3 - 12a^2b + 6ab^2$

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