Evaluasi
-\frac{4xy}{15}
Luaskan
-\frac{4xy}{15}
Bagikan
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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)
Gunakan teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} untuk menjabarkan \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)
Gunakan teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} untuk menjabarkan \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)
Untuk menemukan kebalikan dari \frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2}, temukan kebalikan setiap suku.
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)
Gabungkan \frac{1}{25}y^{2} dan -\frac{64}{225}y^{2} untuk mendapatkan -\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)
Gabungkan -\frac{2}{5}xy dan -\frac{88}{15}yx untuk mendapatkan -\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)
Gabungkan x^{2} dan -\frac{121}{4}x^{2} untuk mendapatkan -\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)
Gunakan teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} untuk menjabarkan \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)
Gabungkan -\frac{117}{4}x^{2} dan \frac{81}{4}x^{2} untuk mendapatkan -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)
Gabungkan -\frac{94}{15}xy dan 6xy untuk mendapatkan -\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)
Gabungkan -\frac{11}{45}y^{2} dan \frac{4}{9}y^{2} untuk mendapatkan \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)
Sederhanakan \left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right). Perkalian dapat diubah menjadi bentuk selisih dua kuadrat menggunakan aturan: \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)
Luaskan \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)
Hitung \frac{1}{5} sampai pangkat 2 dan dapatkan \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)
Luaskan \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)
Hitung 3 sampai pangkat 2 dan dapatkan 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)
Luaskan \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)
Hitung -\frac{2}{5} sampai pangkat 2 dan dapatkan \frac{4}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{5}y^{2}-9x^{2}\right)
Gabungkan \frac{1}{25}y^{2} dan \frac{4}{25}y^{2} untuk mendapatkan \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\frac{1}{5}y^{2}+9x^{2}
Untuk menemukan kebalikan dari \frac{1}{5}y^{2}-9x^{2}, temukan kebalikan setiap suku.
-9x^{2}-\frac{4}{15}xy+9x^{2}
Gabungkan \frac{1}{5}y^{2} dan -\frac{1}{5}y^{2} untuk mendapatkan 0.
-\frac{4}{15}xy
Gabungkan -9x^{2} dan 9x^{2} untuk mendapatkan 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)
Gunakan teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} untuk menjabarkan \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)
Gunakan teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} untuk menjabarkan \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)
Untuk menemukan kebalikan dari \frac{64}{225}y^{2}+\frac{88}{15}yx+\frac{121}{4}x^{2}, temukan kebalikan setiap suku.
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)
Gabungkan \frac{1}{25}y^{2} dan -\frac{64}{225}y^{2} untuk mendapatkan -\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)
Gabungkan -\frac{2}{5}xy dan -\frac{88}{15}yx untuk mendapatkan -\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)
Gabungkan x^{2} dan -\frac{121}{4}x^{2} untuk mendapatkan -\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)
Gunakan teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} untuk menjabarkan \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)
Gabungkan -\frac{117}{4}x^{2} dan \frac{81}{4}x^{2} untuk mendapatkan -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)
Gabungkan -\frac{94}{15}xy dan 6xy untuk mendapatkan -\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)
Gabungkan -\frac{11}{45}y^{2} dan \frac{4}{9}y^{2} untuk mendapatkan \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)
Sederhanakan \left(\frac{1}{5}y-3x\right)\left(3x+\frac{1}{5}y\right). Perkalian dapat diubah menjadi bentuk selisih dua kuadrat menggunakan aturan: \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)
Luaskan \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)
Hitung \frac{1}{5} sampai pangkat 2 dan dapatkan \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)
Luaskan \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)
Hitung 3 sampai pangkat 2 dan dapatkan 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)
Luaskan \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)
Hitung -\frac{2}{5} sampai pangkat 2 dan dapatkan \frac{4}{25}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\left(\frac{1}{5}y^{2}-9x^{2}\right)
Gabungkan \frac{1}{25}y^{2} dan \frac{4}{25}y^{2} untuk mendapatkan \frac{1}{5}y^{2}.
-9x^{2}-\frac{4}{15}xy+\frac{1}{5}y^{2}-\frac{1}{5}y^{2}+9x^{2}
Untuk menemukan kebalikan dari \frac{1}{5}y^{2}-9x^{2}, temukan kebalikan setiap suku.
-9x^{2}-\frac{4}{15}xy+9x^{2}
Gabungkan \frac{1}{5}y^{2} dan -\frac{1}{5}y^{2} untuk mendapatkan 0.
-\frac{4}{15}xy
Gabungkan -9x^{2} dan 9x^{2} untuk mendapatkan 0.
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