8x^3-64-এর সমাধান করুন

$$8 { x }^{ 3 } -64$$

Factor

$$8\left(x-2\right)\left(x^{2}+2x+4\right)$$

Solution Steps

Factor out 8.

$$8\left(x^{3}-8\right)$$

Consider x^{3}-8. Rewrite x^{3}-8 as x^{3}-2^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Rewrite the complete factored expression. Polynomial x^{2}+2x+4 is not factored since it does not have any rational roots.

$$8\left(x-2\right)\left(x^{2}+2x+4\right)$$

Evaluate

$$8\left(x^{3}-8\right)$$