Solve {l}{x(a-b)+y(a-b)}{a(x+c)-b(x+c)}{b(a-1)-(a+1)}

$$\left. \begin{array} { l } { x ( a - b ) + y ( a - b ) } \\ { a ( x + c ) - b ( x + c ) } \\ { b ( a - 1 ) - ( a + 1 ) } \end{array} \right.$$

Least Common Multiple

$$\left(a-b\right)\left(x+c\right)\left(x+y\right)\left(1+b+a-ab\right)$$

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.

$$\left(a-b\right)\left(x+c\right)\left(x+y\right)\left(1+b+a-ab\right)$$

Expand the expression.

$$ab^{2}x^{2}+a^{2}x^{2}-ba^{2}x^{2}+ax^{2}-b^{2}x^{2}-bx^{2}+axyb^{2}-bxya^{2}+xya^{2}+axy-xyb^{2}-bxy+acxb^{2}-bcxa^{2}+cxa^{2}+acx-cxb^{2}-bcx+acyb^{2}-bcya^{2}+cya^{2}+acy-cyb^{2}-bcy$$

Evaluate

$$\left(a-b\right)\left(x+y\right),\ \left(a-b\right)\left(x+c\right),\ b\left(a-1\right)-a-1$$