Solve {l}{(a+b)^2-100}{9-(x-y)^2}

$$\left. \begin{array} { l } { ( a + b ) ^ { 2 } - 100 } \\ { 9 - ( x - y ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(\left(x-y\right)^{2}-9\right)\left(\left(a+b\right)^{2}-100\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(a+b\right)^{2}-100=\left(a+b-10\right)\left(a+b+10\right) 9-\left(x-y\right)^{2}=\left(x-y-3\right)\left(-x+y-3\right)$$

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

$$\left(x-y-3\right)\left(a+b-10\right)\left(x-y+3\right)\left(a+b+10\right)$$

Expand the expression.

$$a^{2}x^{2}+b^{2}x^{2}+2abx^{2}-100x^{2}-4abxy-2xya^{2}-2xyb^{2}+200xy+a^{2}y^{2}+b^{2}y^{2}+2aby^{2}-100y^{2}-18ab-9a^{2}-9b^{2}+900$$

Evaluate

$$\left(a+b\right)^{2}-100,\ -\left(x-y\right)^{2}+9$$