Rešite =2(x+1)^3+4(x+1)^2-3(x+1)+6

$$= 2 ( x + 1 ) ^ { 3 } + 4 ( x + 1 ) ^ { 2 } - 3 ( x + 1 ) + 6$$

Ovrednoti

$$2x^{3}+10x^{2}+11x+9$$

Koraki rešitve

Uporabite binomski izrek \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}, da razširite \left(x+1\right)^{3}.

$$2\left(x^{3}+3x^{2}+3x+1\right)+4\left(x+1\right)^{2}-3\left(x+1\right)+6$$

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

$$2x^{3}+6x^{2}+6x+2+4\left(x+1\right)^{2}-3\left(x+1\right)+6$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(x+1\right)^{2}.

$$2x^{3}+6x^{2}+6x+2+4\left(x^{2}+2x+1\right)-3\left(x+1\right)+6$$

Uporabite distributivnost, da pomnožite 4 s/z x^{2}+2x+1.

$$2x^{3}+6x^{2}+6x+2+4x^{2}+8x+4-3\left(x+1\right)+6$$

Združite 6x^{2} in 4x^{2}, da dobite 10x^{2}.

$$2x^{3}+10x^{2}+6x+2+8x+4-3\left(x+1\right)+6$$

Združite 6x in 8x, da dobite 14x.

$$2x^{3}+10x^{2}+14x+2+4-3\left(x+1\right)+6$$

Seštejte 2 in 4, da dobite 6.

$$2x^{3}+10x^{2}+14x+6-3\left(x+1\right)+6$$

Uporabite distributivnost, da pomnožite -3 s/z x+1.

$$2x^{3}+10x^{2}+14x+6-3x-3+6$$

Združite 14x in -3x, da dobite 11x.

$$2x^{3}+10x^{2}+11x+6-3+6$$

Odštejte 3 od 6, da dobite 3.

$$2x^{3}+10x^{2}+11x+3+6$$

Seštejte 3 in 6, da dobite 9.

$$2x^{3}+10x^{2}+11x+9$$

Razširi

$$2x^{3}+10x^{2}+11x+9$$

Koraki rešitve

Uporabite binomski izrek \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}, da razširite \left(x+1\right)^{3}.

$$2\left(x^{3}+3x^{2}+3x+1\right)+4\left(x+1\right)^{2}-3\left(x+1\right)+6$$

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

$$2x^{3}+6x^{2}+6x+2+4\left(x+1\right)^{2}-3\left(x+1\right)+6$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(x+1\right)^{2}.

$$2x^{3}+6x^{2}+6x+2+4\left(x^{2}+2x+1\right)-3\left(x+1\right)+6$$

Uporabite distributivnost, da pomnožite 4 s/z x^{2}+2x+1.

$$2x^{3}+6x^{2}+6x+2+4x^{2}+8x+4-3\left(x+1\right)+6$$

Združite 6x^{2} in 4x^{2}, da dobite 10x^{2}.

$$2x^{3}+10x^{2}+6x+2+8x+4-3\left(x+1\right)+6$$

Združite 6x in 8x, da dobite 14x.

$$2x^{3}+10x^{2}+14x+2+4-3\left(x+1\right)+6$$

Seštejte 2 in 4, da dobite 6.

$$2x^{3}+10x^{2}+14x+6-3\left(x+1\right)+6$$

Uporabite distributivnost, da pomnožite -3 s/z x+1.

$$2x^{3}+10x^{2}+14x+6-3x-3+6$$

Združite 14x in -3x, da dobite 11x.

$$2x^{3}+10x^{2}+11x+6-3+6$$

Odštejte 3 od 6, da dobite 3.

$$2x^{3}+10x^{2}+11x+3+6$$

Seštejte 3 in 6, da dobite 9.

$$2x^{3}+10x^{2}+11x+9$$