Solve {l}{a^{2}-14a^{2}b^{3}+14a^{3}-2ab^{3}}{a^2}{4a^2y-108xy^2+27y^3}

$$\left. \begin{array} { l } { a ^ { 2 } - 14 a ^ { 2 } b ^ { 3 } + 14 a ^ { 3 } - 2 a b ^ { 3 } } \\ { a ^ { 2 } } \\ { 4 a ^ { 2 } y - 108 x y ^ { 2 } + 27 y ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$ya^{2}\left(4a^{2}+27y^{2}-108xy\right)\left(a+14a^{2}-2b^{3}-14ab^{3}\right)$$

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.

$$ya^{2}\left(4a^{2}+27y^{2}-108xy\right)\left(a+14a^{2}-2b^{3}-14ab^{3}\right)$$

Expand the expression.

$$1512xy^{2}a^{3}b^{3}+216xa^{2}y^{2}b^{3}-1512xy^{2}a^{4}-108xy^{2}a^{3}-378a^{3}b^{3}y^{3}-54a^{2}b^{3}y^{3}+378y^{3}a^{4}+27a^{3}y^{3}-56yb^{3}a^{5}-8yb^{3}a^{4}+56ya^{6}+4ya^{5}$$

Evaluate

$$a\left(a+14a^{2}-2b^{3}-14ab^{3}\right),\ a^{2},\ y\left(4a^{2}+27y^{2}-108xy\right)$$