Rešite (4-x^{2})^2(x^3-2)+x^3(-x^4-2)+32

$$( 4 - x ^ { 2 } ) ^ { 2 } ( x ^ { 3 } - 2 ) + x ^ { 3 } ( - x ^ { 4 } - 2 ) + 32$$

Ovrednoti

$$2x^{2}\left(8+7x-x^{2}-4x^{3}\right)$$

Koraki rešitve

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(4-x^{2}\right)^{2}.

$$\left(16-8x^{2}+\left(x^{2}\right)^{2}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(16-8x^{2}+x^{4}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

Uporabite distributivnost, da pomnožite 16-8x^{2}+x^{4} s/z x^{3}-2.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}-2\right)+32$$

Uporabite distributivnost, da pomnožite x^{3} s/z -x^{4}-2.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)-2x^{3}+32$$

Združite 16x^{3} in -2x^{3}, da dobite 14x^{3}.

$$14x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)+32$$

Seštejte -32 in 32, da dobite 0.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 3 in 4, da dobite 7.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{7}\left(-1\right)$$

Združite x^{7} in x^{7}\left(-1\right), da dobite 0.

$$14x^{3}-8x^{5}+16x^{2}-2x^{4}$$

Razširi

$$16x^{2}+14x^{3}-2x^{4}-8x^{5}$$

Koraki rešitve

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(4-x^{2}\right)^{2}.

$$\left(16-8x^{2}+\left(x^{2}\right)^{2}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(16-8x^{2}+x^{4}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

Uporabite distributivnost, da pomnožite 16-8x^{2}+x^{4} s/z x^{3}-2.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}-2\right)+32$$

Uporabite distributivnost, da pomnožite x^{3} s/z -x^{4}-2.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)-2x^{3}+32$$

Združite 16x^{3} in -2x^{3}, da dobite 14x^{3}.

$$14x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)+32$$

Seštejte -32 in 32, da dobite 0.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 3 in 4, da dobite 7.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{7}\left(-1\right)$$

Združite x^{7} in x^{7}\left(-1\right), da dobite 0.

$$14x^{3}-8x^{5}+16x^{2}-2x^{4}$$