Solve {l}{9xy-12x^{2}y+18y^{2}}{5ab^{2}c^3-10a^2b^3c-20a^3b}

$$\left. \begin{array} { l } { 9 x y - 12 x ^ { 2 } y + 18 y ^ { 2 } } \\ { 5 a b ^ { 2 } c ^ { 3 } - 10 a ^ { 2 } b ^ { 3 } c - 20 a ^ { 3 } b } \end{array} \right.$$

Least Common Multiple

$$15aby\left(16\left(ax\right)^{2}+8ac\left(bx\right)^{2}-24ya^{2}+6byc^{3}-12acyb^{2}-12xa^{2}+3bxc^{3}-6acxb^{2}-4bx^{2}c^{3}\right)$$

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.

$$15aby\left(8acb^{2}x^{2}-4bx^{2}c^{3}+16a^{2}x^{2}-6acxb^{2}+3bxc^{3}-12xa^{2}-12acyb^{2}+6byc^{3}-24ya^{2}\right)$$

Expand the expression.

$$45axyb^{2}c^{3}-90cxya^{2}b^{3}-180bxya^{3}+90ab^{2}y^{2}c^{3}-180ca^{2}y^{2}b^{3}-360by^{2}a^{3}+120cya^{2}x^{2}b^{3}-60ayb^{2}x^{2}c^{3}+240byx^{2}a^{3}$$

Evaluate

$$3y\left(6y+3x-4x^{2}\right),\ 5ab\left(bc^{3}-2acb^{2}-4a^{2}\right)$$