Solve {l}{27a^3-3ab^3}{(x+2)^2-8x}

$$\left. \begin{array} { l } { 27 a ^ { 3 } - 3 a b ^ { 3 } } \\ { ( x + 2 ) ^ { 2 } - 8 x } \end{array} \right.$$

Least Common Multiple

$$3a\left(x-2\right)^{2}\left(b^{3}-9a^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$27a^{3}-3ab^{3}=3a\left(9a^{2}-b^{3}\right)$$

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

$$3a\left(x-2\right)^{2}\left(b^{3}-9a^{2}\right)$$

Expand the expression.

$$3ax^{2}b^{3}-27x^{2}a^{3}-12axb^{3}+108xa^{3}+12ab^{3}-108a^{3}$$

Evaluate

$$27a^{3}-3ab^{3},\ \left(x-2\right)^{2}$$