Solve {l}{a^{2}-2ax+x^2-4b^2}{a(a-2x)+x^2-4b^2}

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

Least Common Multiple

$$\left(a-x\right)^{2}-4b^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$-4b^{2}+\left(a-x\right)^{2}=\left(x-2b-a\right)\left(x-a+2b\right) a^{2}-2ax+x^{2}-4b^{2}=\left(-x+a-2b\right)\left(-x+a+2b\right)$$

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

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

Expand the expression.

$$-x^{2}+2ax-a^{2}+4b^{2}$$

Evaluate

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