Lutasin ang x^6+9x^5+27x^4+27x^3

$$x ^ { 6 } + 9 x ^ { 5 } + 27 x ^ { 4 } + 27 x ^ { 3 }$$

I-factor

$$x^{3}\left(x+3\right)^{3}$$

Mga Hakbang ng Solution

I-factor out ang x^{3}.

$$x^{3}\left(x^{3}+9x^{2}+27x+27\right)$$

Isaalang-alang ang x^{3}+9x^{2}+27x+27. Gamitin ang binomial cube formula na a^{3}+3a^{2}b+3ab^{2}+b^{3}=\left(a+b\right)^{3}, kung saan a=x at b=3.

$$\left(x+3\right)^{3}$$

I-rewrite ang kumpletong naka-factor na expression.

$$x^{3}\left(x+3\right)^{3}$$

I-evaluate

$$\left(x\left(x+3\right)\right)^{3}$$