Whakaoti i te 24y-16y^2

$$24y-16 { y }^{ 2 }$$

Tauwehe

$$8y\left(3-2y\right)$$

Ngā Upane Otinga

Tauwehea te 8.

$$8\left(3y-2y^{2}\right)$$

Whakaarohia te 3y-2y^{2}. Tauwehea te y.

$$y\left(3-2y\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$8y\left(-2y+3\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$-16y^{2}+24y=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$y=\frac{-24±\sqrt{24^{2}}}{2\left(-16\right)}$$

Tuhia te pūtakerua o te 24^{2}.

$$y=\frac{-24±24}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$y=\frac{-24±24}{-32}$$

Nā, me whakaoti te whārite y=\frac{-24±24}{-32} ina he tāpiri te ±. Tāpiri -24 ki te 24.

$$y=\frac{0}{-32}$$

Whakawehe 0 ki te -32.

$$y=0$$

Nā, me whakaoti te whārite y=\frac{-24±24}{-32} ina he tango te ±. Tango 24 mai i -24.

$$y=-\frac{48}{-32}$$

Whakahekea te hautanga \frac{-48}{-32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$y=\frac{3}{2}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 0 mō te x_{1} me te \frac{3}{2} mō te x_{2}.

$$-16y^{2}+24y=-16y\left(y-\frac{3}{2}\right)$$

Tango \frac{3}{2} mai i y mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$-16y^{2}+24y=-16y\times \frac{-2y+3}{-2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te -16 me te -2.

$$-16y^{2}+24y=8y\left(-2y+3\right)$$

Aromātai

$$8y\left(3-2y\right)$$