Whakaoti i te (x-y)(x+y)-(x+y)^2+2y(y-x)

$$( x - y ) ( x + y ) - ( x + y ) ^ { 2 } + 2 y ( y - x )$$

Aromātai

$$-4xy$$

Ngā Upane Otinga

Whakaarohia te \left(x-y\right)\left(x+y\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}-\left(x+y\right)^{2}+2y\left(y-x\right)$$

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

$$x^{2}-y^{2}-\left(x^{2}+2xy+y^{2}\right)+2y\left(y-x\right)$$

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

$$x^{2}-y^{2}-x^{2}-2xy-y^{2}+2y\left(y-x\right)$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-y^{2}-2xy-y^{2}+2y\left(y-x\right)$$

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

$$-2y^{2}-2xy+2y\left(y-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te y-x.

$$-2y^{2}-2xy+2y^{2}-2yx$$

Pahekotia te -2y^{2} me 2y^{2}, ka 0.

$$-2xy-2yx$$

Pahekotia te -2xy me -2yx, ka -4xy.

$$-4xy$$

Whakaroha

$$-4xy$$

Ngā Upane Otinga

Whakaarohia te \left(x-y\right)\left(x+y\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}-\left(x+y\right)^{2}+2y\left(y-x\right)$$

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

$$x^{2}-y^{2}-\left(x^{2}+2xy+y^{2}\right)+2y\left(y-x\right)$$

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

$$x^{2}-y^{2}-x^{2}-2xy-y^{2}+2y\left(y-x\right)$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-y^{2}-2xy-y^{2}+2y\left(y-x\right)$$

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

$$-2y^{2}-2xy+2y\left(y-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te y-x.

$$-2y^{2}-2xy+2y^{2}-2yx$$

Pahekotia te -2y^{2} me 2y^{2}, ka 0.

$$-2xy-2yx$$

Pahekotia te -2xy me -2yx, ka -4xy.

$$-4xy$$