Rešite 3x^2(3x+4)^2+x^3*2(x-1)

$$3 x ^ { 2 } ( 3 x + 4 ) ^ { 2 } + x ^ { 3 } \cdot 2 ( x - 1 )$$

Ovrednoti

$$x^{2}\left(29x^{2}+70x+48\right)$$

Koraki rešitve

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(3x+4\right)^{2}.

$$3x^{2}\left(9x^{2}+24x+16\right)+x^{3}\times 2\left(x-1\right)$$

Uporabite distributivnost, da pomnožite 3x^{2} s/z 9x^{2}+24x+16.

$$27x^{4}+72x^{3}+48x^{2}+x^{3}\times 2\left(x-1\right)$$

Uporabite distributivnost, da pomnožite x^{3}\times 2 s/z x-1.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-x^{3}\times 2$$

Pomnožite -1 in 2, da dobite -2.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-2x^{3}$$

Združite 27x^{4} in 2x^{4}, da dobite 29x^{4}.

$$29x^{4}+72x^{3}+48x^{2}-2x^{3}$$

Združite 72x^{3} in -2x^{3}, da dobite 70x^{3}.

$$29x^{4}+70x^{3}+48x^{2}$$

Razširi

$$29x^{4}+70x^{3}+48x^{2}$$

Koraki rešitve

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(3x+4\right)^{2}.

$$3x^{2}\left(9x^{2}+24x+16\right)+x^{3}\times 2\left(x-1\right)$$

Uporabite distributivnost, da pomnožite 3x^{2} s/z 9x^{2}+24x+16.

$$27x^{4}+72x^{3}+48x^{2}+x^{3}\times 2\left(x-1\right)$$

Uporabite distributivnost, da pomnožite x^{3}\times 2 s/z x-1.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-x^{3}\times 2$$

Pomnožite -1 in 2, da dobite -2.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-2x^{3}$$

Združite 27x^{4} in 2x^{4}, da dobite 29x^{4}.

$$29x^{4}+72x^{3}+48x^{2}-2x^{3}$$

Združite 72x^{3} in -2x^{3}, da dobite 70x^{3}.

$$29x^{4}+70x^{3}+48x^{2}$$