Solve {l}{2a^2+5}{ab+b^2}{(a^2-3b^2)}

$$\left. \begin{array} { l } { 2 a ^ { 2 } + 5 } \\ { a b + b ^ { 2 } } \\ { ( a ^ { 2 } - 3 b ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$-b\left(a+b\right)\left(2a^{2}+5\right)\left(a^{2}-3b^{2}\right)$$

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.

$$-b\left(a+b\right)\left(2a^{2}+5\right)\left(a^{2}-3b^{2}\right)$$

Expand the expression.

$$6a^{3}b^{3}+6a^{2}b^{4}-5a^{2}b^{2}+15ab^{3}+15b^{4}-2b^{2}a^{4}-2ba^{5}-5ba^{3}$$

Evaluate

$$2a^{2}+5,\ b\left(a+b\right),\ a^{2}-3b^{2}$$