Solve {c}{45a^2b-80b^3}{(3a+4b)^2}

$$\left. \begin{array} { c } { 45 a ^ { 2 } b - 80 b ^ { 3 } } \\ { ( 3 a + 4 b ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$-5b\left(3a-4b\right)\left(3a+4b\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$45ba^{2}-80b^{3}=5b\left(3a-4b\right)\left(3a+4b\right)$$

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

$$5b\left(4b-3a\right)\left(3a+4b\right)^{2}$$

Expand the expression.

$$-180a^{2}b^{2}+240ab^{3}+320b^{4}-135ba^{3}$$

Evaluate

$$45ba^{2}-80b^{3},\ \left(3a+4b\right)^{2}$$