Solve {l}{a^{9}-3a^{6}+3a^3-1}{2a^3-bx^3-2ay^3+b}

$$\left. \begin{array} { l } { a ^ { 9 } - 3 a ^ { 6 } + 3 a ^ { 3 } - 1 } \\ { 2 a ^ { 3 } - b x ^ { 3 } - 2 a y ^ { 3 } + b } \end{array} \right.$$

Least Common Multiple

$$\left(bx^{3}+2ay^{3}-2a^{3}-b\right)\left(a^{3}-1\right)^{3}$$

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.

$$\left(a-1\right)^{3}\left(bx^{3}+2ay^{3}-2a^{3}-b\right)\left(a^{2}+a+1\right)^{3}$$

Expand the expression.

$$bx^{3}a^{9}-3bx^{3}a^{6}+3ba^{3}x^{3}-bx^{3}+2y^{3}a^{10}-6y^{3}a^{7}+6y^{3}a^{4}-2ay^{3}-2a^{12}-ba^{9}+6a^{9}+3ba^{6}-6a^{6}-3ba^{3}+2a^{3}+b$$

Evaluate

$$\left(a^{3}-1\right)^{3},\ b+2a^{3}-2ay^{3}-bx^{3}$$