Issolvi =2(x+1)^3+4(x+1)^2-3(x+1)+6

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

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} biex tespandi \left(x+1\right)^{3}.

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'x^{3}+3x^{2}+3x+1.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'x^{2}+2x+1.

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

Ikkombina 6x^{2} u 4x^{2} biex tikseb 10x^{2}.

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

Ikkombina 6x u 8x biex tikseb 14x.

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

Żid 2 u 4 biex tikseb 6.

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

Uża l-propjetà distributtiva biex timmultiplika -3 b'x+1.

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

Ikkombina 14x u -3x biex tikseb 11x.

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

Naqqas 3 minn 6 biex tikseb 3.

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

Żid 3 u 6 biex tikseb 9.

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

Espandi

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} biex tespandi \left(x+1\right)^{3}.

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'x^{3}+3x^{2}+3x+1.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'x^{2}+2x+1.

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

Ikkombina 6x^{2} u 4x^{2} biex tikseb 10x^{2}.

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

Ikkombina 6x u 8x biex tikseb 14x.

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

Żid 2 u 4 biex tikseb 6.

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

Uża l-propjetà distributtiva biex timmultiplika -3 b'x+1.

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

Ikkombina 14x u -3x biex tikseb 11x.

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

Naqqas 3 minn 6 biex tikseb 3.

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

Żid 3 u 6 biex tikseb 9.

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