Lutasin ang x^6-64b^12

$${ x }^{ 6 } -64 { b }^{ 12 }$$

I-factor

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

Mga Hakbang ng Solution

I-rewrite ang x^{6}-64b^{12} bilang \left(x^{3}\right)^{2}-\left(8b^{6}\right)^{2}. Maaaring i-factor ang difference ng mga square gamit ang panuntunang: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x^{3}-8b^{6}\right)\left(x^{3}+8b^{6}\right)$$

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

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

Isaalang-alang ang x^{3}+8b^{6}. I-rewrite ang x^{3}+8b^{6} bilang x^{3}+\left(2b^{2}\right)^{3}. Maaaring i-factor ang sum ng mga cube gamit ang panuntunang: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

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

I-rewrite ang kumpletong naka-factor na expression.

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

I-evaluate

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