Solve {l}{8x^{3}+343y^{3}+84x^{2}y+294xy^{2}}{x^3-125y^3-15x^2y+75xy^2}

$$\left. \begin{array} { l } { 8 x ^ { 3 } + 343 y ^ { 3 } + 84 x ^ { 2 } y + 294 x y ^ { 2 } } \\ { x ^ { 3 } - 125 y ^ { 3 } - 15 x ^ { 2 } y + 75 x y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$-8x^{6}-6405x^{2}y^{4}+11025xy^{5}+42875y^{6}+366y^{2}x^{4}+36yx^{5}-1233\left(xy\right)^{3}$$

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.

$$36yx^{5}+366y^{2}x^{4}+42875y^{6}+11025xy^{5}-6405x^{2}y^{4}-1233x^{3}y^{3}-8x^{6}$$

Expand the expression.

$$-8x^{6}-1233x^{3}y^{3}-6405x^{2}y^{4}+11025xy^{5}+42875y^{6}+366y^{2}x^{4}+36yx^{5}$$

Evaluate

$$\left(2x+7y\right)^{3},\ \left(x-5y\right)^{3}$$