Question
Factorize the polynomial:
$8 a^3-b^3-12 a^2 b+6 a b^2$
$8 a^3-b^3-12 a^2 b+6 a b^2$
✓
Answer
$8 a^3-b^3-12 a^2 b+6 a b^2$
The expression $8 a^3-b^3-12 a^2 b+6 a b^2$ can also be written as $=(2 a)^3-(b)^3-3 \times 2 a \times 2 a \times b+3 \times 2 a \times b \times b$ $=(2 a)^3-(b)^3-3 \times 2 a \times b(2 a-b)$.
Using identity $(x-y)^3=x^3-y^3-3 x y(x-y)$ with respect to the expression $(2 a)^3-(b)^3-3 \times 2 a \times b(2 a-b)$, we get $(2 a-b)^3$
Therefore, after factorizing the expression $8 a^3-b^3-12 a^2 b+6 a b^2$, weget $(2 a-b)^3$
The expression $8 a^3-b^3-12 a^2 b+6 a b^2$ can also be written as $=(2 a)^3-(b)^3-3 \times 2 a \times 2 a \times b+3 \times 2 a \times b \times b$ $=(2 a)^3-(b)^3-3 \times 2 a \times b(2 a-b)$.
Using identity $(x-y)^3=x^3-y^3-3 x y(x-y)$ with respect to the expression $(2 a)^3-(b)^3-3 \times 2 a \times b(2 a-b)$, we get $(2 a-b)^3$
Therefore, after factorizing the expression $8 a^3-b^3-12 a^2 b+6 a b^2$, weget $(2 a-b)^3$
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