Solve {l}{2a^2+4ab}{C2a^2+2ab}{D2a^2+2ab+2b^2}

$$\left. \begin{array} { l } { 2 a ^ { 2 } + 4 a b } \\ { C 2 a ^ { 2 } + 2 a b } \\ { D 2 a ^ { 2 } + 2 a b + 2 b ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$2a\left(a+2b\right)\left(C_{2}a+2b\right)\left(D_{2}a^{2}+2ab+2b^{2}\right)$$

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.

$$2a\left(a+2b\right)\left(C_{2}a+2b\right)\left(D_{2}a^{2}+2ab+2b^{2}\right)$$

Expand the expression.

$$2C_{2}D_{2}a^{5}+4C_{2}D_{2}ba^{4}+8C_{2}a^{2}b^{3}+12C_{2}b^{2}a^{3}+4C_{2}ba^{4}+8D_{2}b^{2}a^{3}+4D_{2}ba^{4}+24a^{2}b^{3}+16ab^{4}+8b^{2}a^{3}$$

Evaluate

$$2a\left(a+2b\right),\ a\left(C_{2}a+2b\right),\ D_{2}a^{2}+2ab+2b^{2}$$