Solve {l}{ab^2-bc^2-ab+c^2}{(x-2y)^2+4x-8y}

$$\left. \begin{array} { l } { a b ^ { 2 } - b c ^ { 2 } - a b + c ^ { 2 } } \\ { ( x - 2 y ) ^ { 2 } + 4 x - 8 y } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$bc^{2}x^{2}+abx^{2}-ab^{2}x^{2}-c^{2}x^{2}+4axyb^{2}-4bxyc^{2}+4xyc^{2}-4abxy+4bxc^{2}-4axb^{2}+4abx-4xc^{2}+4bc^{2}y^{2}-4ab^{2}y^{2}+4aby^{2}-4c^{2}y^{2}+8ayb^{2}-8byc^{2}+8yc^{2}-8aby$$

Evaluate

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