Выражение: (a*(1//2)+b*(1//2))^2-2*a*b*(1//2)
Ответ: a^2*(1//4)-(1//2)*a*b+b^2*(1//4)
Решаем по действиям:1. (a*(1//2)+b*(1//2))^2=a^2*(1//4)+(1//2)*a*b+b^2*(1//4) (a*(1//2)+b*(1//2))^2=((a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))) 1.1. (a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))=a^2*(1//4)+(1//2)*a*b+b^2*(1//4) (a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))=a*(1//2)*a*(1//2)+a*(1//2)*b*(1//2)+b*(1//2)*a*(1//2)+b*(1//2)*b*(1//2) 1.1.1. a*a=a^2 a*a=a^(1+1) 1.1.1.1. 1+1=2 +1 _1_ 2 1.1.2. (1//2)*(1//2)=(1//4) 1.1.3. (1//2)*(1//2)=(1//4) 1.1.4. (1//2)*(1//2)=(1//4) 1.1.5. a*(1//4)*b+b*(1//4)*a=(1//2)*a*b 1.1.6. b*b=b^2 b*b=b^(1+1) 1.1.6.1. 1+1=2 +1 _1_ 2 1.1.7. (1//2)*(1//2)=(1//4)2. 2*(1//2)=13. (1//2)*a*b-a*b=-(1//2)*a*b
Решаем по шагам:1. a^2*(1//4)+(1//2)*a*b+b^2*(1//4)-2*a*b*(1//2) 1.1. (a*(1//2)+b*(1//2))^2=a^2*(1//4)+(1//2)*a*b+b^2*(1//4) (a*(1//2)+b*(1//2))^2=((a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))) 1.1.1. (a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))=a^2*(1//4)+(1//2)*a*b+b^2*(1//4) (a*(1//2)+b*(1//2))*(a*(1//2)+b*(1//2))=a*(1//2)*a*(1//2)+a*(1//2)*b*(1//2)+b*(1//2)*a*(1//2)+b*(1//2)*b*(1//2) 1.1.1.1. a*a=a^2 a*a=a^(1+1) 1.1.1.1.1. 1+1=2 +1 _1_ 2 1.1.1.2. (1//2)*(1//2)=(1//4) 1.1.1.3. (1//2)*(1//2)=(1//4) 1.1.1.4. (1//2)*(1//2)=(1//4) 1.1.1.5. a*(1//4)*b+b*(1//4)*a=(1//2)*a*b 1.1.1.6. b*b=b^2 b*b=b^(1+1) 1.1.1.6.1. 1+1=2 +1 _1_ 2 1.1.1.7. (1//2)*(1//2)=(1//4)2. a^2*(1//4)+(1//2)*a*b+b^2*(1//4)-a*b 2.1. 2*(1//2)=13. a^2*(1//4)-(1//2)*a*b+b^2*(1//4) 3.1. (1//2)*a*b-a*b=-(1//2)*a*b
Приводим к окончательному ответу с возможной потерей точности:
Окончательный ответ: a^2*0.25-0.5*a*b+b^2*0.25
По действиям: 1. 1//4=0.25 1.0|4_ _ 8_|0.25 20 2_0_ 0 2. 1//2=0.5 1.0|2_ _ 1_0_|0.5 0 3. 1//4=0.25 1.0|4_ _ 8_|0.25 20 2_0_ 0
По шагам: 1. a^2*0.25-(1//2)*a*b+b^2*(1//4) 1.1. 1//4=0.25 1.0|4_ _ 8_|0.25 20 2_0_ 0 2. a^2*0.25-0.5*a*b+b^2*(1//4) 2.1. 1//2=0.5 1.0|2_ _ 1_0_|0.5 0 3. a^2*0.25-0.5*a*b+b^2*0.25 3.1. 1//4=0.25 1.0|4_ _ 8_|0.25 20 2_0_ 0