Lutasin ang x^6y^6-x^3y^3

$$x ^ { 6 } y ^ { 6 } - x ^ { 3 } y ^ { 3 }$$

I-factor

$$x^{3}y^{3}\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

Mga Hakbang ng Solution

I-factor out ang x^{3}y^{3}.

$$x^{3}y^{3}\left(x^{3}y^{3}-1\right)$$

Isaalang-alang ang x^{3}y^{3}-1. I-rewrite ang x^{3}y^{3}-1 bilang \left(xy\right)^{3}-1^{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).

$$\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

I-rewrite ang kumpletong naka-factor na expression.

$$x^{3}y^{3}\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

I-evaluate

$$\left(xy\right)^{3}\left(\left(xy\right)^{3}-1\right)$$