Solve {l}{16a^2b-64b^3}{p^4-256}

$$\left. \begin{array} { l } { 16 a ^ { 2 } b - 64 b ^ { 3 } } \\ { p ^ { 4 } - 256 } \end{array} \right.$$

Least Common Multiple

$$-16b\left(a^{2}-4b^{2}\right)\left(p^{4}-256\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$16ba^{2}-64b^{3}=16b\left(a-2b\right)\left(a+2b\right) p^{4}-256=\left(p-4\right)\left(p+4\right)\left(p^{2}+16\right)$$

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

$$16b\left(p-4\right)\left(a-2b\right)\left(p+4\right)\left(a+2b\right)\left(-p^{2}-16\right)$$

Expand the expression.

$$-16ba^{2}p^{4}+64b^{3}p^{4}+4096ba^{2}-16384b^{3}$$

Evaluate

$$16b\left(a^{2}-4b^{2}\right),\ p^{4}-256$$