Whakaoti i te (x-1/2)(x+2)+(x-1/3)(x+3)-x(25/6+x)

$$( x - \frac { 1 } { 2 } ) ( x + 2 ) + ( x - \frac { 1 } { 3 } ) ( x + 3 ) - x ( \frac { 25 } { 6 } + x )$$

Aromātai

$$x^{2}-2$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-\frac{1}{2} ki ia tau o x+2.

$$x^{2}+2x-\frac{1}{2}x-\frac{1}{2}\times 2+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

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

$$x^{2}+\frac{3}{2}x-\frac{1}{2}\times 2+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

Me whakakore te 2 me te 2.

$$x^{2}+\frac{3}{2}x-1+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-\frac{1}{3} ki ia tau o x+3.

$$x^{2}+\frac{3}{2}x-1+x^{2}+3x-\frac{1}{3}x-\frac{1}{3}\times 3-x\left(\frac{25}{6}+x\right)$$

Pahekotia te 3x me -\frac{1}{3}x, ka \frac{8}{3}x.

$$x^{2}+\frac{3}{2}x-1+x^{2}+\frac{8}{3}x-\frac{1}{3}\times 3-x\left(\frac{25}{6}+x\right)$$

Me whakakore te 3 me te 3.

$$x^{2}+\frac{3}{2}x-1+x^{2}+\frac{8}{3}x-1-x\left(\frac{25}{6}+x\right)$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}+\frac{3}{2}x-1+\frac{8}{3}x-1-x\left(\frac{25}{6}+x\right)$$

Pahekotia te \frac{3}{2}x me \frac{8}{3}x, ka \frac{25}{6}x.

$$2x^{2}+\frac{25}{6}x-1-1-x\left(\frac{25}{6}+x\right)$$

Tangohia te 1 i te -1, ka -2.

$$2x^{2}+\frac{25}{6}x-2-x\left(\frac{25}{6}+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te \frac{25}{6}+x.

$$2x^{2}+\frac{25}{6}x-2-\left(x\times \frac{25}{6}+x^{2}\right)$$

Hei kimi i te tauaro o x\times \frac{25}{6}+x^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}+\frac{25}{6}x-2-x\times \frac{25}{6}-x^{2}$$

Whakareatia te -1 ki te \frac{25}{6}, ka -\frac{25}{6}.

$$2x^{2}+\frac{25}{6}x-2-\frac{25}{6}x-x^{2}$$

Pahekotia te \frac{25}{6}x me -\frac{25}{6}x, ka 0.

$$2x^{2}-2-x^{2}$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-2$$

Whakaroha

$$x^{2}-2$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-\frac{1}{2} ki ia tau o x+2.

$$x^{2}+2x-\frac{1}{2}x-\frac{1}{2}\times 2+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

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

$$x^{2}+\frac{3}{2}x-\frac{1}{2}\times 2+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

Me whakakore te 2 me te 2.

$$x^{2}+\frac{3}{2}x-1+\left(x-\frac{1}{3}\right)\left(x+3\right)-x\left(\frac{25}{6}+x\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-\frac{1}{3} ki ia tau o x+3.

$$x^{2}+\frac{3}{2}x-1+x^{2}+3x-\frac{1}{3}x-\frac{1}{3}\times 3-x\left(\frac{25}{6}+x\right)$$

Pahekotia te 3x me -\frac{1}{3}x, ka \frac{8}{3}x.

$$x^{2}+\frac{3}{2}x-1+x^{2}+\frac{8}{3}x-\frac{1}{3}\times 3-x\left(\frac{25}{6}+x\right)$$

Me whakakore te 3 me te 3.

$$x^{2}+\frac{3}{2}x-1+x^{2}+\frac{8}{3}x-1-x\left(\frac{25}{6}+x\right)$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}+\frac{3}{2}x-1+\frac{8}{3}x-1-x\left(\frac{25}{6}+x\right)$$

Pahekotia te \frac{3}{2}x me \frac{8}{3}x, ka \frac{25}{6}x.

$$2x^{2}+\frac{25}{6}x-1-1-x\left(\frac{25}{6}+x\right)$$

Tangohia te 1 i te -1, ka -2.

$$2x^{2}+\frac{25}{6}x-2-x\left(\frac{25}{6}+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te \frac{25}{6}+x.

$$2x^{2}+\frac{25}{6}x-2-\left(x\times \frac{25}{6}+x^{2}\right)$$

Hei kimi i te tauaro o x\times \frac{25}{6}+x^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}+\frac{25}{6}x-2-x\times \frac{25}{6}-x^{2}$$

Whakareatia te -1 ki te \frac{25}{6}, ka -\frac{25}{6}.

$$2x^{2}+\frac{25}{6}x-2-\frac{25}{6}x-x^{2}$$

Pahekotia te \frac{25}{6}x me -\frac{25}{6}x, ka 0.

$$2x^{2}-2-x^{2}$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-2$$