Solve {l}{6ax+15b^2y^2-6b^2x}{-15ay^2}

$$\left. \begin{array}{l}{ 6 a x + 15 b ^ { 2 } y ^ { 2 } - 6 b ^ { 2 } x }\\{ - 15 a y ^ { 2 } }\end{array} \right.$$

Least Common Multiple

$$15ay^{2}\left(5\left(by\right)^{2}+2ax-2xb^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$6ax+15b^{2}y^{2}-6b^{2}x=3\left(-2xb^{2}+2ax+5b^{2}y^{2}\right)$$

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

$$15ay^{2}\left(5b^{2}y^{2}+2ax-2xb^{2}\right)$$

Expand the expression.

$$-30axb^{2}y^{2}+30xa^{2}y^{2}+75ab^{2}y^{4}$$

Evaluate

$$15\left(by\right)^{2}+6ax-6xb^{2},\ -15ay^{2}$$