Issolvi (2x+1/3y)(x-3y)-(2x+y)(1/2x-y)=

$$( 2 x + \frac { 1 } { 3 } y ) ( x - 3 y ) - ( 2 x + y ) ( \frac { 1 } { 2 } x - y ) =$$

Evalwa

$$-\frac{25xy}{6}+x^{2}$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 2x+\frac{1}{3}y b'kull terminu ta' x-3y.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y\left(-3\right)y-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Immultiplika y u y biex tikseb y^{2}.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Ikkombina -6xy u \frac{1}{3}yx biex tikseb -\frac{17}{3}xy.

$$2x^{2}-\frac{17}{3}xy+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Immultiplika \frac{1}{3} u -3 biex tikseb \frac{-3}{3}.

$$2x^{2}-\frac{17}{3}xy+\frac{-3}{3}y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Iddividi -3 b'3 biex tikseb-1.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 2x+y b'kull terminu ta' \frac{1}{2}x-y.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x\times \frac{1}{2}x-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Immultiplika x u x biex tikseb x^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x^{2}\times \frac{1}{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Annulla 2 u 2.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Ikkombina -2xy u y\times \frac{1}{2}x biex tikseb -\frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-\frac{3}{2}xy-y^{2}\right)$$

Biex issib l-oppost ta' x^{2}-\frac{3}{2}xy-y^{2}, sib l-oppost ta' kull terminu.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}-\left(-\frac{3}{2}xy\right)-\left(-y^{2}\right)$$

L-oppost ta' -\frac{3}{2}xy huwa \frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy-\left(-y^{2}\right)$$

L-oppost ta' -y^{2} huwa y^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy+y^{2}$$

Ikkombina 2x^{2} u -x^{2} biex tikseb x^{2}.

$$x^{2}-\frac{17}{3}xy-y^{2}+\frac{3}{2}xy+y^{2}$$

Ikkombina -\frac{17}{3}xy u \frac{3}{2}xy biex tikseb -\frac{25}{6}xy.

$$x^{2}-\frac{25}{6}xy-y^{2}+y^{2}$$

Ikkombina -y^{2} u y^{2} biex tikseb 0.

$$x^{2}-\frac{25}{6}xy$$

Espandi

$$-\frac{25xy}{6}+x^{2}$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 2x+\frac{1}{3}y b'kull terminu ta' x-3y.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y\left(-3\right)y-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Immultiplika y u y biex tikseb y^{2}.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Ikkombina -6xy u \frac{1}{3}yx biex tikseb -\frac{17}{3}xy.

$$2x^{2}-\frac{17}{3}xy+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Immultiplika \frac{1}{3} u -3 biex tikseb \frac{-3}{3}.

$$2x^{2}-\frac{17}{3}xy+\frac{-3}{3}y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Iddividi -3 b'3 biex tikseb-1.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 2x+y b'kull terminu ta' \frac{1}{2}x-y.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x\times \frac{1}{2}x-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Immultiplika x u x biex tikseb x^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x^{2}\times \frac{1}{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Annulla 2 u 2.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Ikkombina -2xy u y\times \frac{1}{2}x biex tikseb -\frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-\frac{3}{2}xy-y^{2}\right)$$

Biex issib l-oppost ta' x^{2}-\frac{3}{2}xy-y^{2}, sib l-oppost ta' kull terminu.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}-\left(-\frac{3}{2}xy\right)-\left(-y^{2}\right)$$

L-oppost ta' -\frac{3}{2}xy huwa \frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy-\left(-y^{2}\right)$$

L-oppost ta' -y^{2} huwa y^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy+y^{2}$$

Ikkombina 2x^{2} u -x^{2} biex tikseb x^{2}.

$$x^{2}-\frac{17}{3}xy-y^{2}+\frac{3}{2}xy+y^{2}$$

Ikkombina -\frac{17}{3}xy u \frac{3}{2}xy biex tikseb -\frac{25}{6}xy.

$$x^{2}-\frac{25}{6}xy-y^{2}+y^{2}$$

Ikkombina -y^{2} u y^{2} biex tikseb 0.

$$x^{2}-\frac{25}{6}xy$$