Solve {l}{a^{4}+2a^{2}b+b^{2}}{x^4-Ab^2x^3+4b^4}

$$\left. \begin{array} { l } { a ^ { 4 } + 2 a ^ { 2 } b + b ^ { 2 } } \\ { x ^ { 4 } - A b ^ { 2 } x ^ { 3 } + 4 b ^ { 4 } } \end{array} \right.$$

Least Common Multiple

$$\left(a^{2}+b\right)^{2}\left(-x^{4}+Ab^{2}x^{3}-4b^{4}\right)$$

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.

$$\left(a^{2}+b\right)^{2}\left(-x^{4}+Ab^{2}x^{3}-4b^{4}\right)$$

Expand the expression.

$$-a^{4}x^{4}-2ba^{2}x^{4}-b^{2}x^{4}+Ab^{2}x^{3}a^{4}+2Aa^{2}b^{3}x^{3}+Ax^{3}b^{4}-4a^{4}b^{4}-8a^{2}b^{5}-4b^{6}$$

Evaluate

$$\left(a^{2}+b\right)^{2},\ x^{4}-Ab^{2}x^{3}+4b^{4}$$