Solve {l}{3x^{2}y^{3}-9x^3y^2}{3ax-bx-3ay+by}{x^3+5x^2+x+5}

$$\left. \begin{array} { l } { 3 x ^ { 2 } y ^ { 3 } - 9 x ^ { 3 } y ^ { 2 } } \\ { 3 a x - b x - 3 a y + b y } \\ { x ^ { 3 } + 5 x ^ { 2 } + x + 5 } \end{array} \right.$$

Least Common Multiple

$$-3\left(x+5\right)\left(x-y\right)\left(3a-b\right)\left(3x-y\right)\left(x^{2}+1\right)\left(xy\right)^{2}$$

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.

$$-3\left(x+5\right)\left(x-y\right)\left(3a-b\right)\left(3x-y\right)x^{2}y^{2}\left(x^{2}+1\right)$$

Expand the expression.

$$15bx^{4}y^{4}-45ax^{4}y^{4}+3bx^{3}y^{4}-9ax^{3}y^{4}+180ax^{3}y^{3}-60bx^{3}y^{3}+15bx^{2}y^{4}-45ax^{2}y^{4}+3by^{4}x^{5}-9ay^{4}x^{5}+36ay^{3}x^{6}-12by^{3}x^{6}+180ay^{3}x^{5}-60by^{3}x^{5}+36ay^{3}x^{4}-12by^{3}x^{4}+9by^{2}x^{7}-27ay^{2}x^{7}+45by^{2}x^{6}-135ay^{2}x^{6}+9by^{2}x^{5}-27ay^{2}x^{5}+45by^{2}x^{4}-135ay^{2}x^{4}$$

Evaluate

$$3\left(y-3x\right)\left(xy\right)^{2},\ \left(x-y\right)\left(3a-b\right),\ \left(x+5\right)\left(x^{2}+1\right)$$