Solve {l}{ax+ay-b}{bx-ab+b}{-3(a-b)^2}

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

Least Common Multiple

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

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.

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

Expand the expression.

$$6a^{2}b^{2}x^{2}-3ax^{2}b^{3}-3bx^{2}a^{3}+6xya^{2}b^{2}-3axyb^{3}-3bxya^{3}+3xa^{2}b^{3}+3bxa^{4}-6xb^{2}a^{3}+9xa^{2}b^{2}-9axb^{3}-3bxa^{3}+3xb^{4}+3ya^{2}b^{3}+3bya^{4}-6yb^{2}a^{3}+6ya^{2}b^{2}-3ayb^{3}-3bya^{3}+6a^{2}b^{3}-3b^{2}a^{3}-3ab^{4}+3a^{2}b^{2}-6ab^{3}+3b^{4}$$

Evaluate

$$ax+ay-b,\ b\left(x-a+1\right),\ -3\left(a-b\right)^{2}$$