Solve {l}{(x-10)(x^2+10x+100)}{y^3+(7-y)(49-7y+y^2)}

$$\left. \begin{array} { l } { ( x - 10 ) ( x ^ { 2 } + 10 x + 100 ) } \\ { y ^ { 3 } + ( 7 - y ) ( 49 - 7 y + y ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$7\left(2y^{2}-14y+49\right)\left(x^{3}-1000\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}-1000=\left(x-10\right)\left(x^{2}+10x+100\right) 14y^{2}-98y+343=7\left(2y^{2}-14y+49\right)$$

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

$$7\left(x-10\right)\left(2y^{2}-14y+49\right)\left(x^{2}+10x+100\right)$$

Expand the expression.

$$343x^{3}+14y^{2}x^{3}-14000y^{2}-98yx^{3}+98000y-343000$$

Evaluate

$$x^{3}-1000,\ 14y^{2}-98y+343$$