Solve {l}{4p^2-9q^2}{x^2+xy+8x+8y}

$$\left. \begin{array} { l } { 4 p ^ { 2 } - 9 q ^ { 2 } } \\ { x ^ { 2 } + x y + 8 x + 8 y } \end{array} \right.$$

Least Common Multiple

$$-\left(x+8\right)\left(x+y\right)\left(4p^{2}-9q^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$4p^{2}-9q^{2}=\left(2p-3q\right)\left(2p+3q\right)$$

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

$$-\left(x+8\right)\left(2p-3q\right)\left(x+y\right)\left(2p+3q\right)$$

Expand the expression.

$$9q^{2}x^{2}-4p^{2}x^{2}+9xyq^{2}-4xyp^{2}+72xq^{2}-32xp^{2}+72yq^{2}-32yp^{2}$$

Evaluate

$$4p^{2}-9q^{2},\ \left(x+8\right)\left(x+y\right)$$