Solve 5a^3-20a,a^3-3a^2-10a,a^2(a-1)-2a+8

$$5 a ^ { 3 } - 20 a , a ^ { 3 } - 3 a ^ { 2 } - 10 a , a ^ { 2 } ( a - 1 ) - 2 a + 8$$

Least Common Multiple

$$5a\left(a-5\right)\left(a^{2}-4\right)\left(a^{2}-3a+4\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$5a\left(a^{2}-4\right)=5a\left(a-2\right)\left(a+2\right)$$

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

$$5a\left(a-5\right)\left(a-2\right)\left(a+2\right)\left(a^{2}-3a+4\right)$$

Expand the expression.

$$5a^{6}-40a^{5}+75a^{4}+60a^{3}-380a^{2}+400a$$

Evaluate

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