Solve {l}{x^2-8x-33-14y-y^2}{(x^2+y+3)(x^2-y+1)}

$$\left. \begin{array} { l } { x ^ { 2 } - 8 x - 33 - 14 y - y ^ { 2 } } \\ { ( x ^ { 2 } + y + 3 ) ( x ^ { 2 } - y + 1 ) } \end{array} \right.$$

Least Common Multiple

$$\left(x-y-11\right)\left(x+y+3\right)\left(x^{2}-y+1\right)\left(x^{2}+y+3\right)$$

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.

$$\left(x-y-11\right)\left(x+y+3\right)\left(x^{2}-y+1\right)\left(x^{2}+y+3\right)$$

Expand the expression.

$$x^{6}-8x^{5}-29x^{4}-32x^{3}-5x^{2}y^{2}-129x^{2}+8xy^{2}+16xy-24x+y^{4}+16y^{3}-y^{2}x^{4}+58y^{2}-14yx^{4}-58yx^{2}+24y-99$$

Evaluate

$$\left(x-y-11\right)\left(x+y+3\right),\ \left(x^{2}-y+1\right)\left(x^{2}+y+3\right)$$