Solve {l}{(2a-5b)^2}{3(a+4b)(a-4b)}

$$\left. \begin{array} { l } { ( 2 a - 5 b ) ^ { 2 } } \\ { 3 ( a + 4 b ) ( a - 4 b ) } \end{array} \right.$$

Least Common Multiple

$$-3\left(2a-5b\right)^{2}\left(a^{2}-16b^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$3a^{2}-48b^{2}=3\left(a-4b\right)\left(a+4b\right)$$

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

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

Expand the expression.

$$-12a^{4}+117a^{2}b^{2}-960ab^{3}+1200b^{4}+60ba^{3}$$

Evaluate

$$\left(2a-5b\right)^{2},\ 3\left(a^{2}-16b^{2}\right)$$