Whakaoti i te =w^20.05^2+(1-w)^20.08^2+2w(1-w)*0.3*0.05*0.08

$$= w ^ { 2 } 0.05 ^ { 2 } + ( 1 - w ) ^ { 2 } 0.08 ^ { 2 } + 2 w ( 1 - w ) \times 0.3 \times 0.05 \times 0.08$$

Aromātai

$$\frac{13w^{2}}{2000}-\frac{13w}{1250}+0.0064$$

Ngā Upane Otinga

Tātaihia te 0.05 mā te pū o 2, kia riro ko 0.0025.

$$w^{2}\times 0.0025+\left(1-w\right)^{2}\times 0.08^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

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

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.08^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Tātaihia te 0.08 mā te pū o 2, kia riro ko 0.0064.

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.0064+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1-2w+w^{2} ki te 0.0064.

$$w^{2}\times 0.0025+0.0064-0.0128w+0.0064w^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Pahekotia te w^{2}\times 0.0025 me 0.0064w^{2}, ka 0.0089w^{2}.

$$0.0089w^{2}+0.0064-0.0128w+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Whakareatia te 2 ki te 0.3, ka 0.6.

$$0.0089w^{2}+0.0064-0.0128w+0.6w\left(1-w\right)\times 0.05\times 0.08$$

Whakareatia te 0.6 ki te 0.05, ka 0.03.

$$0.0089w^{2}+0.0064-0.0128w+0.03w\left(1-w\right)\times 0.08$$

Whakareatia te 0.03 ki te 0.08, ka 0.0024.

$$0.0089w^{2}+0.0064-0.0128w+0.0024w\left(1-w\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 0.0024w ki te 1-w.

$$0.0089w^{2}+0.0064-0.0128w+0.0024w-0.0024w^{2}$$

Pahekotia te -0.0128w me 0.0024w, ka -0.0104w.

$$0.0089w^{2}+0.0064-0.0104w-0.0024w^{2}$$

Pahekotia te 0.0089w^{2} me -0.0024w^{2}, ka 0.0065w^{2}.

$$0.0065w^{2}+0.0064-0.0104w$$

Whakaroha

$$\frac{13w^{2}}{2000}-\frac{13w}{1250}+0.0064$$

Ngā Upane Otinga

Tātaihia te 0.05 mā te pū o 2, kia riro ko 0.0025.

$$w^{2}\times 0.0025+\left(1-w\right)^{2}\times 0.08^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

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

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.08^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Tātaihia te 0.08 mā te pū o 2, kia riro ko 0.0064.

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.0064+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1-2w+w^{2} ki te 0.0064.

$$w^{2}\times 0.0025+0.0064-0.0128w+0.0064w^{2}+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Pahekotia te w^{2}\times 0.0025 me 0.0064w^{2}, ka 0.0089w^{2}.

$$0.0089w^{2}+0.0064-0.0128w+2w\left(1-w\right)\times 0.3\times 0.05\times 0.08$$

Whakareatia te 2 ki te 0.3, ka 0.6.

$$0.0089w^{2}+0.0064-0.0128w+0.6w\left(1-w\right)\times 0.05\times 0.08$$

Whakareatia te 0.6 ki te 0.05, ka 0.03.

$$0.0089w^{2}+0.0064-0.0128w+0.03w\left(1-w\right)\times 0.08$$

Whakareatia te 0.03 ki te 0.08, ka 0.0024.

$$0.0089w^{2}+0.0064-0.0128w+0.0024w\left(1-w\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 0.0024w ki te 1-w.

$$0.0089w^{2}+0.0064-0.0128w+0.0024w-0.0024w^{2}$$

Pahekotia te -0.0128w me 0.0024w, ka -0.0104w.

$$0.0089w^{2}+0.0064-0.0104w-0.0024w^{2}$$

Pahekotia te 0.0089w^{2} me -0.0024w^{2}, ka 0.0065w^{2}.

$$0.0065w^{2}+0.0064-0.0104w$$