Issolvi (x+11)^2+(y-5)^2-(x-y)

$$( x + 11 ) ^ { 2 } + ( y - 5 ) ^ { 2 } - ( x - y )$$

Evalwa

$$\left(x+11\right)^{2}+\left(y-5\right)^{2}+y-x$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+11\right)^{2}.

$$x^{2}+22x+121+\left(y-5\right)^{2}-\left(x-y\right)$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(y-5\right)^{2}.

$$x^{2}+22x+121+y^{2}-10y+25-\left(x-y\right)$$

Żid 121 u 25 biex tikseb 146.

$$x^{2}+22x+146+y^{2}-10y-\left(x-y\right)$$

Biex issib l-oppost ta' x-y, sib l-oppost ta' kull terminu.

$$x^{2}+22x+146+y^{2}-10y-x+y$$

Ikkombina 22x u -x biex tikseb 21x.

$$x^{2}+21x+146+y^{2}-10y+y$$

Ikkombina -10y u y biex tikseb -9y.

$$x^{2}+21x+146+y^{2}-9y$$

Espandi

$$x^{2}+21x+y^{2}-9y+146$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+11\right)^{2}.

$$x^{2}+22x+121+\left(y-5\right)^{2}-\left(x-y\right)$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(y-5\right)^{2}.

$$x^{2}+22x+121+y^{2}-10y+25-\left(x-y\right)$$

Żid 121 u 25 biex tikseb 146.

$$x^{2}+22x+146+y^{2}-10y-\left(x-y\right)$$

Biex issib l-oppost ta' x-y, sib l-oppost ta' kull terminu.

$$x^{2}+22x+146+y^{2}-10y-x+y$$

Ikkombina 22x u -x biex tikseb 21x.

$$x^{2}+21x+146+y^{2}-10y+y$$

Ikkombina -10y u y biex tikseb -9y.

$$x^{2}+21x+146+y^{2}-9y$$