Solve {l}{a^{2}-4b^2+a^3-8b^3-(a-2b)^2}{++4}

$$\left. \begin{array}{l}{ a ^ { 2 } - 4 b ^ { 2 } + a ^ { 3 } - 8 b ^ { 3 } - ( a - 2 b ) ^ { 2 } }\\{ + + 4 }\end{array} \right.$$

Least Common Multiple

$$32b^{2}+32b^{3}-16ab-4a^{3}$$

Solution Steps

Factor the expressions that are not already factored.

$$a^{3}-8b^{2}+4ab-8b^{3}=\left(a-2b\right)\left(a^{2}+2ab+4b^{2}+4b\right) 4=2^{2}$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$4\left(a-2b\right)\left(-a^{2}-2ab-4b^{2}-4b\right)$$

Expand the expression.

$$-4a^{3}-16ab+32b^{3}+32b^{2}$$

Evaluate

$$a^{3}+4ab-8b^{3}-8b^{2},\ 4$$