Solve {l}{(x+2y)(x-2y)-(x+y)^2}{(a+b+c)(a+b-c)}

$$\left. \begin{array} { l } { ( x + 2 y ) ( x - 2 y ) - ( x + y ) ^ { 2 } } \\ { ( a + b + c ) ( a + b - c ) } \end{array} \right.$$

Least Common Multiple

$$y\left(2x+5y\right)\left(-\left(-a-b\right)^{2}+c^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(a+b\right)^{2}-c^{2}=\left(a+b+c\right)\left(a+b-c\right)$$

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

$$y\left(c-a-b\right)\left(2x+5y\right)\left(a+b+c\right)$$

Expand the expression.

$$2xyc^{2}-4abxy-2xya^{2}-2xyb^{2}+5c^{2}y^{2}-10aby^{2}-5a^{2}y^{2}-5b^{2}y^{2}$$

Evaluate

$$-y\left(2x+5y\right),\ \left(a+b\right)^{2}-c^{2}$$