Resol 1/4(x+y)^2-9/16(x-y)^2

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

Calcula

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

Passos de solució

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(x+y\right)^{2}.

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

Utilitzeu la propietat distributiva per multiplicar \frac{1}{4} per x^{2}+2xy+y^{2}.

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

Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-y\right)^{2}.

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

Utilitzeu la propietat distributiva per multiplicar -\frac{9}{16} per x^{2}-2xy+y^{2}.

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

Combineu \frac{1}{4}x^{2} i -\frac{9}{16}x^{2} per obtenir -\frac{5}{16}x^{2}.

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

Combineu \frac{1}{2}xy i \frac{9}{8}xy per obtenir \frac{13}{8}xy.

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

Combineu \frac{1}{4}y^{2} i -\frac{9}{16}y^{2} per obtenir -\frac{5}{16}y^{2}.

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

Expandiu

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

Passos de solució

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(x+y\right)^{2}.

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

Utilitzeu la propietat distributiva per multiplicar \frac{1}{4} per x^{2}+2xy+y^{2}.

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

Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-y\right)^{2}.

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

Utilitzeu la propietat distributiva per multiplicar -\frac{9}{16} per x^{2}-2xy+y^{2}.

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

Combineu \frac{1}{4}x^{2} i -\frac{9}{16}x^{2} per obtenir -\frac{5}{16}x^{2}.

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

Combineu \frac{1}{2}xy i \frac{9}{8}xy per obtenir \frac{13}{8}xy.

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

Combineu \frac{1}{4}y^{2} i -\frac{9}{16}y^{2} per obtenir -\frac{5}{16}y^{2}.

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