Solve {l}{4x^2+4xy+y^2-4}{(x+y)(x-y)+(x+y)^2}

$$\left. \begin{array} { l } { 4 x ^ { 2 } + 4 x y + y ^ { 2 } - 4 } \\ { ( x + y ) ( x - y ) + ( x + y ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$2x\left(x+y\right)\left(\left(2x+y\right)^{2}-4\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-4+\left(2x+y\right)^{2}=\left(2x+y-2\right)\left(2x+y+2\right) 2x^{2}+2xy=2x\left(x+y\right)$$

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

$$2x\left(x+y\right)\left(2x+y-2\right)\left(2x+y+2\right)$$

Expand the expression.

$$8x^{4}+10x^{2}y^{2}-8x^{2}+2xy^{3}-8xy+16yx^{3}$$

Evaluate

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