Lutasin ang 216m^6-27n^6

$$216 m ^ { 6 } - 27 n ^ { 6 }$$

I-factor

$$27\left(2m^{2}-n^{2}\right)\left(4m^{4}+2m^{2}n^{2}+n^{4}\right)$$

Mga Hakbang ng Solution

I-factor out ang 27.

$$27\left(8m^{6}-n^{6}\right)$$

Isaalang-alang ang 8m^{6}-n^{6}. I-rewrite ang 8m^{6}-n^{6} bilang \left(2m^{2}\right)^{3}-\left(n^{2}\right)^{3}. Maaaring i-factor ang difference ng mga cube gamit ang panuntunang: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

I-rewrite ang kumpletong naka-factor na expression.

$$27\left(2m^{2}-n^{2}\right)\left(4m^{4}+2m^{2}n^{2}+n^{4}\right)$$

I-evaluate

$$216m^{6}-27n^{6}$$