Solve {l}{(a^2+8)^2}{(b^2+9)^2}

$$\left. \begin{array} { l } { ( a ^ { 2 } + 8 ) ^ { 2 } } \\ { ( b ^ { 2 } + 9 ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(\left(a^{2}+8\right)\left(b^{2}+9\right)\right)^{2}$$

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.

$$\left(a^{2}+8\right)^{2}\left(b^{2}+9\right)^{2}$$

Expand the expression.

$$a^{4}b^{4}+81a^{4}+16a^{2}b^{4}+288a^{2}b^{2}+1296a^{2}+64b^{4}+18b^{2}a^{4}+1152b^{2}+5184$$

Evaluate

$$\left(a^{2}+8\right)^{2},\ \left(b^{2}+9\right)^{2}$$