Solve {l}{2a^{2}b+3ab^{2}-4b^{3}-3a^{3}+3a^{2}b-3ab^2-4b^3}{5x+6+8x-9+4x^2+10+3x^2-2}

$$\left. \begin{array} { l } { 2 a ^ { 2 } b + 3 a b ^ { 2 } - 4 b ^ { 3 } - 3 a ^ { 3 } + 3 a ^ { 2 } b - 3 a b ^ { 2 } - 4 b ^ { 3 } } \\ { 5 x + 6 + 8 x - 9 + 4 x ^ { 2 } + 10 + 3 x ^ { 2 } - 2 } \end{array} \right.$$

Least Common Multiple

$$\left(a+b\right)\left(40b^{2}+15a^{2}-40ab+56\left(bx\right)^{2}+21\left(ax\right)^{2}+104xb^{2}+39xa^{2}-104abx-56abx^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$5a^{2}b-8b^{3}-3a^{3}=\left(a+b\right)\left(-3a^{2}+8ab-8b^{2}\right) 13x+7x^{2}+5=7\left(x-\left(-\frac{1}{14}\sqrt{29}-\frac{13}{14}\right)\right)\left(x-\left(\frac{1}{14}\sqrt{29}-\frac{13}{14}\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(a+b\right)\left(40b^{2}+15a^{2}-40ab+104xb^{2}+39xa^{2}-104abx+56b^{2}x^{2}+21a^{2}x^{2}-56abx^{2}\right)$$

Expand the expression.

$$-35ba^{2}x^{2}+21x^{2}a^{3}+56x^{2}b^{3}-65bxa^{2}+39xa^{3}+104xb^{3}-25ba^{2}+15a^{3}+40b^{3}$$

Evaluate

$$5ba^{2}-3a^{3}-8b^{3},\ 7x^{2}+13x+5$$