Factorise each of the following 8a³-b³-12a²b+6ab²

Let's factorize the expression:

\[
8a^3 - b^3 - 12a^2b + 6ab^2
\]

Step 1: Group terms that can be factored together.

\[
(8a^3 - 12a^2b) - (b^3 - 6ab^2)
\]

Step 2: Factor out common factors from each group.

\[
4a^2(2a - 3b) - b^2(b - 6a)
\]

Step 3: Rewrite the expression in terms of a common factor if possible. Notice that both groups have a factor involving \((2a - b)\):

\[
4a^2(2a - 3b) - b^2(3b - 2a)
\]

Therefore, the factorization of \(8a^3 - b^

Factorise each of the following 8a³ - b³ - 12a²b + 6ab²

This page provides a step-by-step solution to factorizing the cubic polynomial 8a³ - b³ - 12a²b + 6ab². The problem demonstrates the use of the grouping method and the difference of cubes formula, suitable for students in Grades 10-12.

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