Solve {l}{(a-b)quad4(a-b)}{x(x+y)+9(x+y+1)+x}

$$\left. \begin{array} { l } { ( a - b ) \quad 4 ( a - b ) } \\ { x ( x + y ) + 9 ( x + y + 1 ) + x } \end{array} \right.$$

Least Common Multiple

$$4\left(x+9\right)\left(x+y+1\right)\left(a-b\right)^{2}$$

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.

$$4\left(x+9\right)\left(x+y+1\right)\left(a-b\right)^{2}$$

Expand the expression.

$$4a^{2}x^{2}+4b^{2}x^{2}-8abx^{2}+4xya^{2}+4xyb^{2}-8abxy+40xa^{2}+40xb^{2}-80abx+36ya^{2}+36yb^{2}-72aby-72ab+36a^{2}+36b^{2}$$

Evaluate

$$4\left(a-b\right)^{2},\ \left(x+9\right)\left(x+y+1\right)$$