Solve {l}{(7x+4y)^2+(4x-7y)^2}{(7x+4y)^2-(7y+4x)}

$$\left\{ \begin{array} { l } { ( 7 x + 4 y ) ^ { 2 } + ( 4 x - 7 y ) ^ { 2 } } \\ { ( 7 x + 4 y ) ^ { 2 } - ( 7 y + 4 x ) } \end{array} \right.$$

Least Common Multiple

$$65\left(x^{2}+y^{2}\right)\left(\left(7x+4y\right)^{2}-4x-7y\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$65x^{2}+65y^{2}=65\left(x^{2}+y^{2}\right)$$

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

$$65\left(x^{2}+y^{2}\right)\left(49x^{2}+56xy-4x+16y^{2}-7y\right)$$

Expand the expression.

$$3185x^{4}-260x^{3}+4225x^{2}y^{2}+3640xy^{3}-260xy^{2}+1040y^{4}-455y^{3}+3640yx^{3}-455yx^{2}$$

Evaluate

$$65\left(x^{2}+y^{2}\right),\ \left(7x+4y\right)^{2}-4x-7y$$