Solve {l}{(x-y)^2+(x-y)}{14a(8+z)^3+7a(8+z)}

$$\left. \begin{array} { l } { ( x - y ) ^ { 2 } + ( x - y ) } \\ { 14 a ( 8 + z ) ^ { 3 } + 7 a ( 8 + z ) } \end{array} \right.$$

Least Common Multiple

$$7a\left(x-y\right)\left(z+8\right)\left(x-y+1\right)\left(2z^{2}+32z+129\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$7a\left(8+z\right)\left(2\left(8+z\right)^{2}+1\right)=7a\left(z+8\right)\left(2z^{2}+32z+129\right)$$

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

$$7a\left(x-y\right)\left(z+8\right)\left(x-y+1\right)\left(2z^{2}+32z+129\right)$$

Expand the expression.

$$14ax^{2}z^{3}+336ax^{2}z^{2}+7224ax^{2}-28axyz^{3}-672axyz^{2}-5390axyz-14448axy+14axz^{3}+336axz^{2}+2695axz+7224ax+14ay^{2}z^{3}+336ay^{2}z^{2}+7224ay^{2}-14ayz^{3}-336ayz^{2}-2695ayz-7224ay+2695azx^{2}+2695azy^{2}$$

Evaluate

$$\left(x-y\right)\left(x-y+1\right),\ 7a\left(z+8\right)\left(2\left(z+8\right)^{2}+1\right)$$