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

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

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

$$8a^{2}+6ab+2b^{2}=2\left(4a^{2}+3ab+b^{2}\right)$$

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

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

Expand the expression.

$$64a^{5}+6a^{2}b^{3}+2ab^{4}+24b^{2}a^{3}+48ba^{4}$$

Evaluate

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