Solve {l}{4x^2-9y^2}{3ax+6ay-bx-2by}

$$\left. \begin{array} { l } { 4 x ^ { 2 } - 9 y ^ { 2 } } \\ { 3 a x + 6 a y - b x - 2 b y } \end{array} \right.$$

Least Common Multiple

$$\left(3a-b\right)\left(x+2y\right)\left(4x^{2}-9y^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$4x^{2}-9y^{2}=\left(2x-3y\right)\left(2x+3y\right)$$

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

$$\left(2x-3y\right)\left(3a-b\right)\left(x+2y\right)\left(2x+3y\right)$$

Expand the expression.

$$12ax^{3}-4bx^{3}+9bxy^{2}-27axy^{2}+18by^{3}-54ay^{3}+24ayx^{2}-8byx^{2}$$

Evaluate

$$4x^{2}-9y^{2},\ \left(3a-b\right)\left(x+2y\right)$$