Resolver -81a^4b^4+16c^4

$$- 81 a ^ { 4 } b ^ { 4 } + 16 c ^ { 4 }$$

Faktorizatu

$$\left(3ab-2c\right)\left(3ab+2c\right)\left(-9a^{2}b^{2}-4c^{2}\right)$$

Ebazpidea

Berridatzi -81a^{4}b^{4}+16c^{4} honela: \left(4c^{2}\right)^{2}-\left(9a^{2}b^{2}\right)^{2}. Kuboen diferentzia faktorizatzeko, erabili p^{2}-q^{2}=\left(p-q\right)\left(p+q\right) araua.

$$\left(4c^{2}-9a^{2}b^{2}\right)\left(4c^{2}+9a^{2}b^{2}\right)$$

Berrantolatu gaiak.

$$\left(-9a^{2}b^{2}+4c^{2}\right)\left(9a^{2}b^{2}+4c^{2}\right)$$

Kasurako: -9a^{2}b^{2}+4c^{2}. Berridatzi -9a^{2}b^{2}+4c^{2} honela: \left(2c\right)^{2}-\left(3ab\right)^{2}. Kuboen diferentzia faktorizatzeko, erabili p^{2}-q^{2}=\left(p-q\right)\left(p+q\right) araua.

$$\left(2c-3ab\right)\left(2c+3ab\right)$$

Berrantolatu gaiak.

$$\left(-3ab+2c\right)\left(3ab+2c\right)$$

Berridatzi faktorizatutako adierazpen osoa.

$$\left(-3ab+2c\right)\left(3ab+2c\right)\left(9a^{2}b^{2}+4c^{2}\right)$$

Ebaluatu

$$16c^{4}-81\left(ab\right)^{4}$$