Solve {l}{(y^2+3)(y^3-5)}{(5t-7)(2t+8)}

$$\left. \begin{array} { l } { ( y ^ { 2 } + 3 ) ( y ^ { 3 } - 5 ) } \\ { ( 5 t - 7 ) ( 2 t + 8 ) } \end{array} \right.$$

Least Common Multiple

$$2\left(5t-7\right)\left(t+4\right)\left(y^{2}+3\right)\left(y^{3}-5\right)$$

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.

$$2\left(5t-7\right)\left(t+4\right)\left(y^{2}+3\right)\left(y^{3}-5\right)$$

Expand the expression.

$$10t^{2}y^{5}+26ty^{5}-56y^{5}+30t^{2}y^{3}+78ty^{3}-168y^{3}-50t^{2}y^{2}-130ty^{2}+280y^{2}-150t^{2}-390t+840$$

Evaluate

$$\left(y^{2}+3\right)\left(y^{3}-5\right),\ 2\left(5t-7\right)\left(t+4\right)$$