Solve {l}{(x+5)^2-5(x-1)(x-5)}{f(y-3)^2-2(y-2)^2}

$$\left. \begin{array} { l } { ( x + 5 ) ^ { 2 } - 5 ( x - 1 ) ( x - 5 ) } \\ { f ( y - 3 ) ^ { 2 } - 2 ( y - 2 ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$4x\left(x-10\right)\left(fy^{2}-6fy-2\left(y-2\right)^{2}+9f\right)$$

Solution Steps

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

$$4x\left(x-10\right)\left(fy^{2}-2y^{2}-6fy+8y+9f-8\right)$$

Expand the expression.

$$4fx^{2}y^{2}-8x^{2}y^{2}+36fx^{2}-32x^{2}-40fxy^{2}+80xy^{2}+240fxy-360fx-320xy+320x-24fyx^{2}+32yx^{2}$$

Evaluate

$$4x\left(10-x\right),\ f\left(y-3\right)^{2}-2\left(y-2\right)^{2}$$