Whakaoti i te 1/2x(3-x)+3(x+1)(x-1)-x(x-1)^2+(x-1)^3-1/2(2x-8)

$$\frac { 1 } { 2 } x ( 3 - x ) + 3 ( x + 1 ) ( x - 1 ) - x ( x - 1 ) ^ { 2 } + ( x - 1 ) ^ { 3 } - \frac { 1 } { 2 } ( 2 x - 8 )$$

Aromātai

$$\frac{x\left(3x+5\right)}{2}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2}x ki te 3-x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+3 ki te x-1 ka whakakotahi i ngā kupu rite.

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

Pahekotia te -\frac{1}{2}x^{2} me 3x^{2}, ka \frac{5}{2}x^{2}.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x^{2}-2x+1\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x^{2}-2x+1.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-\left(x^{3}-2x^{2}+x\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Hei kimi i te tauaro o x^{3}-2x^{2}+x, kimihia te tauaro o ia taurangi.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x^{3}+2x^{2}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{5}{2}x^{2} me 2x^{2}, ka \frac{9}{2}x^{2}.

$$\frac{3}{2}x+\frac{9}{2}x^{2}-3-x^{3}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{3}{2}x me -x, ka \frac{1}{2}x.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(x-1\right)^{3}.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+x^{3}-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te -x^{3} me x^{3}, ka 0.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{9}{2}x^{2} me -3x^{2}, ka \frac{3}{2}x^{2}.

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

Pahekotia te \frac{1}{2}x me 3x, ka \frac{7}{2}x.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-3-1-\frac{1}{2}\left(2x-8\right)$$

Tangohia te 1 i te -3, ka -4.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{2} ki te 2x-8.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-x+4$$

Pahekotia te \frac{7}{2}x me -x, ka \frac{5}{2}x.

$$\frac{5}{2}x+\frac{3}{2}x^{2}-4+4$$

Tāpirihia te -4 ki te 4, ka 0.

$$\frac{5}{2}x+\frac{3}{2}x^{2}$$

Whakaroha

$$\frac{3x^{2}+5x}{2}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2}x ki te 3-x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+3 ki te x-1 ka whakakotahi i ngā kupu rite.

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

Pahekotia te -\frac{1}{2}x^{2} me 3x^{2}, ka \frac{5}{2}x^{2}.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x^{2}-2x+1\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x^{2}-2x+1.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-\left(x^{3}-2x^{2}+x\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Hei kimi i te tauaro o x^{3}-2x^{2}+x, kimihia te tauaro o ia taurangi.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x^{3}+2x^{2}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{5}{2}x^{2} me 2x^{2}, ka \frac{9}{2}x^{2}.

$$\frac{3}{2}x+\frac{9}{2}x^{2}-3-x^{3}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{3}{2}x me -x, ka \frac{1}{2}x.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(x-1\right)^{3}.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+x^{3}-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te -x^{3} me x^{3}, ka 0.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

Pahekotia te \frac{9}{2}x^{2} me -3x^{2}, ka \frac{3}{2}x^{2}.

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

Pahekotia te \frac{1}{2}x me 3x, ka \frac{7}{2}x.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-3-1-\frac{1}{2}\left(2x-8\right)$$

Tangohia te 1 i te -3, ka -4.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{2} ki te 2x-8.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-x+4$$

Pahekotia te \frac{7}{2}x me -x, ka \frac{5}{2}x.

$$\frac{5}{2}x+\frac{3}{2}x^{2}-4+4$$

Tāpirihia te -4 ki te 4, ka 0.

$$\frac{5}{2}x+\frac{3}{2}x^{2}$$