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

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

Factor

$$5a\left(a-2\right)\left(a+2\right)$$

Solution Steps

Factor out 5.

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

Consider a^{3}-4a. Factor out a.

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

Consider a^{2}-4. Rewrite a^{2}-4 as a^{2}-2^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-2\right)\left(a+2\right)$$

Rewrite the complete factored expression.

$$5a\left(a-2\right)\left(a+2\right)$$

Evaluate

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