Solve {l}{3a^{3}+9a^2-120a}{x^4-3x^2y-10y^2}

$$\left. \begin{array} { l } { 3 a ^ { 3 } + 9 a ^ { 2 } - 120 a } \\ { x ^ { 4 } - 3 x ^ { 2 } y - 10 y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$3a\left(5-a\right)\left(a+8\right)\left(x^{2}-5y\right)\left(x^{2}+2y\right)$$

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.

$$3a\left(5-a\right)\left(a+8\right)\left(x^{2}-5y\right)\left(x^{2}+2y\right)$$

Expand the expression.

$$-3a^{3}x^{4}-9a^{2}x^{4}+120ax^{4}+30y^{2}a^{3}+90a^{2}y^{2}-1200ay^{2}+9yx^{2}a^{3}+27ya^{2}x^{2}-360ayx^{2}$$

Evaluate

$$3a\left(a-5\right)\left(a+8\right),\ \left(x^{2}-5y\right)\left(x^{2}+2y\right)$$