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x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\left(\frac{8}{15}y+\frac{11}{2}x\right)^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(x-\frac{1}{5}y\right)^{2}.
x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\left(\frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2}\right)+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, lai izvērstu \left(\frac{8}{15}y+\frac{11}{2}x\right)^{2}.
x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\frac{64}{225}y^{2}-\frac{88}{15}yx-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lai atrastu \frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.
x^{2}-\frac{2}{5}xy-\frac{11}{45}y^{2}-\frac{88}{15}yx-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet \frac{1}{25}y^{2} un -\frac{64}{225}y^{2}, lai iegūtu -\frac{11}{45}y^{2}.
x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{2}{5}xy un -\frac{88}{15}yx, lai iegūtu -\frac{94}{15}xy.
-\frac{117}{4}x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet x^{2} un -\frac{121}{4}x^{2}, lai iegūtu -\frac{117}{4}x^{2}.
-\frac{117}{4}x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+\frac{81}{4}x^{2}+6xy+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, lai izvērstu \left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}.
-9x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+6xy+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{117}{4}x^{2} un \frac{81}{4}x^{2}, lai iegūtu -9x^{2}.
-9x^{2}-\frac{4}{15}xy-\frac{11}{45}y^{2}+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{94}{15}xy un 6xy, lai iegūtu -\frac{4}{15}xy.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{11}{45}y^{2} un \frac{4}{9}y^{2}, lai iegūtu \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}y\right)^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Apsveriet \left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right). Reizināšanu var pārvērst par kvadrātu starpību, izmantojot šo kārtulu: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}\right)^{2}y^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Paplašiniet \left(\frac{1}{5}y\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Aprēķiniet \frac{1}{5} pakāpē 2 un iegūstiet \frac{1}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-3^{2}x^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Paplašiniet \left(3x\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Aprēķiniet 3 pakāpē 2 un iegūstiet 9.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\left(-\frac{2}{5}\right)^{2}y^{2}\right)
Paplašiniet \left(-\frac{2}{5}y\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\frac{4}{25}y^{2}\right)
Aprēķiniet -\frac{2}{5} pakāpē 2 un iegūstiet \frac{4}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{5}y^{2}-9x^{2}\right)
Savelciet \frac{1}{25}y^{2} un \frac{4}{25}y^{2}, lai iegūtu \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\frac{1}{5}y^{2}+9x^{2}
Lai atrastu \frac{1}{5}y^{2}-9x^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.
-9x^{2}-\frac{4}{15}xy+9x^{2}
Savelciet \frac{1}{5}y^{2} un -\frac{1}{5}y^{2}, lai iegūtu 0.
-\frac{4}{15}xy
Savelciet -9x^{2} un 9x^{2}, lai iegūtu 0.
x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\left(\frac{8}{15}y+\frac{11}{2}x\right)^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(x-\frac{1}{5}y\right)^{2}.
x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\left(\frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2}\right)+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, lai izvērstu \left(\frac{8}{15}y+\frac{11}{2}x\right)^{2}.
x^{2}-\frac{2}{5}xy+\frac{1}{25}y^{2}-\frac{64}{225}y^{2}-\frac{88}{15}yx-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lai atrastu \frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.
x^{2}-\frac{2}{5}xy-\frac{11}{45}y^{2}-\frac{88}{15}yx-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet \frac{1}{25}y^{2} un -\frac{64}{225}y^{2}, lai iegūtu -\frac{11}{45}y^{2}.
x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}-\frac{121}{4}x^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{2}{5}xy un -\frac{88}{15}yx, lai iegūtu -\frac{94}{15}xy.
-\frac{117}{4}x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+\left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet x^{2} un -\frac{121}{4}x^{2}, lai iegūtu -\frac{117}{4}x^{2}.
-\frac{117}{4}x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+\frac{81}{4}x^{2}+6xy+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Lietojiet Ņūtona binomu \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, lai izvērstu \left(\frac{9}{2}x+\frac{2}{3}y\right)^{2}.
-9x^{2}-\frac{94}{15}xy-\frac{11}{45}y^{2}+6xy+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{117}{4}x^{2} un \frac{81}{4}x^{2}, lai iegūtu -9x^{2}.
-9x^{2}-\frac{4}{15}xy-\frac{11}{45}y^{2}+\frac{4}{9}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{94}{15}xy un 6xy, lai iegūtu -\frac{4}{15}xy.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right)+\left(-\frac{2}{5}y\right)^{2}\right)
Savelciet -\frac{11}{45}y^{2} un \frac{4}{9}y^{2}, lai iegūtu \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}y\right)^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Apsveriet \left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right). Reizināšanu var pārvērst par kvadrātu starpību, izmantojot šo kārtulu: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\left(\frac{1}{5}\right)^{2}y^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Paplašiniet \left(\frac{1}{5}y\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-\left(3x\right)^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Aprēķiniet \frac{1}{5} pakāpē 2 un iegūstiet \frac{1}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-3^{2}x^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Paplašiniet \left(3x\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\left(-\frac{2}{5}y\right)^{2}\right)
Aprēķiniet 3 pakāpē 2 un iegūstiet 9.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\left(-\frac{2}{5}\right)^{2}y^{2}\right)
Paplašiniet \left(-\frac{2}{5}y\right)^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{25}y^{2}-9x^{2}+\frac{4}{25}y^{2}\right)
Aprēķiniet -\frac{2}{5} pakāpē 2 un iegūstiet \frac{4}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{5}y^{2}-9x^{2}\right)
Savelciet \frac{1}{25}y^{2} un \frac{4}{25}y^{2}, lai iegūtu \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\frac{1}{5}y^{2}+9x^{2}
Lai atrastu \frac{1}{5}y^{2}-9x^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.
-9x^{2}-\frac{4}{15}xy+9x^{2}
Savelciet \frac{1}{5}y^{2} un -\frac{1}{5}y^{2}, lai iegūtu 0.
-\frac{4}{15}xy
Savelciet -9x^{2} un 9x^{2}, lai iegūtu 0.