Solve {l}{49a^{4}+b^{6}+a^{2}-14a^{2}b^{3}+14a^{3}-2ab^{3}}{(7a^{2}-b^{3}+a)^{2}}{-64x^3+144x^2y-108xy^2+27y^3}

$$\left. \begin{array} { l } { 49 a ^ { 4 } + b ^ { 6 } + a ^ { 2 } - 14 a ^ { 2 } b ^ { 3 } + 14 a ^ { 3 } - 2 a b ^ { 3 } } \\ { ( 7 a ^ { 2 } - b ^ { 3 } + a ) ^ { 2 } } \\ { - 64 x ^ { 3 } + 144 x ^ { 2 } y - 108 x y ^ { 2 } + 27 y ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$-\left(4x-3y\right)^{3}\left(a+7a^{2}-b^{3}\right)^{2}$$

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.

$$-\left(4x-3y\right)^{3}\left(a+7a^{2}-b^{3}\right)^{2}$$

Expand the expression.

$$-64x^{3}b^{6}+896a^{2}b^{3}x^{3}+128ab^{3}x^{3}-3136x^{3}a^{4}-896a^{3}x^{3}-64a^{2}x^{3}-108xy^{2}b^{6}+1512xa^{2}y^{2}b^{3}+216axy^{2}b^{3}-5292xy^{2}a^{4}-1512xy^{2}a^{3}-108xa^{2}y^{2}+27y^{3}b^{6}-378a^{2}b^{3}y^{3}-54ab^{3}y^{3}+1323y^{3}a^{4}+378a^{3}y^{3}+27a^{2}y^{3}+144yx^{2}b^{6}-2016ya^{2}x^{2}b^{3}-288ayx^{2}b^{3}+7056yx^{2}a^{4}+2016yx^{2}a^{3}+144ya^{2}x^{2}$$

Evaluate

$$\left(a+7a^{2}-b^{3}\right)^{2},\ \left(a+7a^{2}-b^{3}\right)^{2},\ -\left(4x-3y\right)^{3}$$