Whakaoti i te 1/4(x+y)^2-9/16(x-y)^2

$$\frac { 1 } { 4 } ( x + y ) ^ { 2 } - \frac { 9 } { 16 } ( x - y ) ^ { 2 }$$

Aromātai

$$\frac{\left(5x-y\right)\left(5y-x\right)}{16}$$

Ngā Upane Otinga

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}\right)-\frac{9}{16}\left(x-y\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x^{2}+2xy+y^{2}.

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}\left(x-y\right)^{2}$$

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

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}\left(x^{2}-2xy+y^{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{9}{16} ki te x^{2}-2xy+y^{2}.

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}x^{2}+\frac{9}{8}xy-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{4}x^{2} me -\frac{9}{16}x^{2}, ka -\frac{5}{16}x^{2}.

$$-\frac{5}{16}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}+\frac{9}{8}xy-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{2}xy me \frac{9}{8}xy, ka \frac{13}{8}xy.

$$-\frac{5}{16}x^{2}+\frac{13}{8}xy+\frac{1}{4}y^{2}-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{4}y^{2} me -\frac{9}{16}y^{2}, ka -\frac{5}{16}y^{2}.

$$-\frac{5}{16}x^{2}+\frac{13}{8}xy-\frac{5}{16}y^{2}$$

Whakaroha

$$\frac{13xy}{8}-\frac{5x^{2}}{16}-\frac{5y^{2}}{16}$$

Ngā Upane Otinga

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}\right)-\frac{9}{16}\left(x-y\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x^{2}+2xy+y^{2}.

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}\left(x-y\right)^{2}$$

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

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}\left(x^{2}-2xy+y^{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{9}{16} ki te x^{2}-2xy+y^{2}.

$$\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}-\frac{9}{16}x^{2}+\frac{9}{8}xy-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{4}x^{2} me -\frac{9}{16}x^{2}, ka -\frac{5}{16}x^{2}.

$$-\frac{5}{16}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}+\frac{9}{8}xy-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{2}xy me \frac{9}{8}xy, ka \frac{13}{8}xy.

$$-\frac{5}{16}x^{2}+\frac{13}{8}xy+\frac{1}{4}y^{2}-\frac{9}{16}y^{2}$$

Pahekotia te \frac{1}{4}y^{2} me -\frac{9}{16}y^{2}, ka -\frac{5}{16}y^{2}.

$$-\frac{5}{16}x^{2}+\frac{13}{8}xy-\frac{5}{16}y^{2}$$