(18a^4b+60a^3b^2+48a^2b^3):6a^2b-(a+b)(3a+7b)

Выражение: (18*a^4*b+60*a^3*b^2+48*a^2*b^3):6*a^2*b-(a+b)*(3*a+7*b) Ответ: 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-a^2*3-10*a*b-b^2*7 Решаем по действиям: 1. (18*a^4*b+60*a^3*b^2+48*a^2*b^3):6=18*a^4*b/6+60*a^3*b^2/6+48*a^2*b^3/6 2. 18/6=3 18|6_ _ 1_8_|3 0 3. 60/6=10 60|6_ _ 6_ |10 0 4. 48/6=8 48|6_ _ 4_8_|8 0 5. (3*a^4*b+10*a^3*b^2+8*a^2*b^3)*a^2=3*a^6*b+10*a^5*b^2+8*a^4*b^3 (3*a^4*b+10*a^3*b^2+8*a^2*b^3)*a^2=3*a^4*b*a^2+10*a^3*b^2*a^2+8*a^2*b^3*a^2 5.1. a^4*a^2=a^6 a^4*a^2=a^(4+2) 5.1.1. 4+2=6 +4 _2_ 6 5.2. a^3*a^2=a^5 a^3*a^2=a^(3+2) 5.2.1. 3+2=5 +3 _2_ 5 5.3. a^2*a^2=a^4 a^2*a^2=a^(2+2) 5.3.1. 2+2=4 +2 _2_ 4 6. (3*a^6*b+10*a^5*b^2+8*a^4*b^3)*b=3*a^6*b^2+10*a^5*b^3+8*a^4*b^4 (3*a^6*b+10*a^5*b^2+8*a^4*b^3)*b=3*a^6*b*b+10*a^5*b^2*b+8*a^4*b^3*b 6.1. b*b=b^2 b*b=b^(1+1) 6.1.1. 1+1=2 +1 _1_ 2 6.2. b^2*b=b^3 b^2*b=b^(2+1) 6.2.1. 2+1=3 +2 _1_ 3 6.3. b^3*b=b^4 b^3*b=b^(3+1) 6.3.1. 3+1=4 +3 _1_ 4 7. (a+b)*(3*a+7*b)=a^2*3+10*a*b+b^2*7 (a+b)*(3*a+7*b)=a*3*a+a*7*b+b*3*a+b*7*b 7.1. a*a=a^2 a*a=a^(1+1) 7.1.1. 1+1=2 +1 _1_ 2 7.2. a*7*b+b*3*a=10*a*b 7.3. b*b=b^2 b*b=b^(1+1) 7.3.1. 1+1=2 +1 _1_ 2 8. 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-(a^2*3+10*a*b+b^2*7)=3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-a^2*3-10*a*b-b^2*7 Решаем по шагам: 1. (18*a^4*b/6+60*a^3*b^2/6+48*a^2*b^3/6)*a^2*b-(a+b)*(3*a+7*b) 1.1. (18*a^4*b+60*a^3*b^2+48*a^2*b^3):6=18*a^4*b/6+60*a^3*b^2/6+48*a^2*b^3/6 2. (3*a^4*b+60*a^3*b^2/6+48*a^2*b^3/6)*a^2*b-(a+b)*(3*a+7*b) 2.1. 18/6=3 18|6_ _ 1_8_|3 0 3. (3*a^4*b+10*a^3*b^2+48*a^2*b^3/6)*a^2*b-(a+b)*(3*a+7*b) 3.1. 60/6=10 60|6_ _ 6_ |10 0 4. (3*a^4*b+10*a^3*b^2+8*a^2*b^3)*a^2*b-(a+b)*(3*a+7*b) 4.1. 48/6=8 48|6_ _ 4_8_|8 0 5. (3*a^6*b+10*a^5*b^2+8*a^4*b^3)*b-(a+b)*(3*a+7*b) 5.1. (3*a^4*b+10*a^3*b^2+8*a^2*b^3)*a^2=3*a^6*b+10*a^5*b^2+8*a^4*b^3 (3*a^4*b+10*a^3*b^2+8*a^2*b^3)*a^2=3*a^4*b*a^2+10*a^3*b^2*a^2+8*a^2*b^3*a^2 5.1.1. a^4*a^2=a^6 a^4*a^2=a^(4+2) 5.1.1.1. 4+2=6 +4 _2_ 6 5.1.2. a^3*a^2=a^5 a^3*a^2=a^(3+2) 5.1.2.1. 3+2=5 +3 _2_ 5 5.1.3. a^2*a^2=a^4 a^2*a^2=a^(2+2) 5.1.3.1. 2+2=4 +2 _2_ 4 6. 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-(a+b)*(3*a+7*b) 6.1. (3*a^6*b+10*a^5*b^2+8*a^4*b^3)*b=3*a^6*b^2+10*a^5*b^3+8*a^4*b^4 (3*a^6*b+10*a^5*b^2+8*a^4*b^3)*b=3*a^6*b*b+10*a^5*b^2*b+8*a^4*b^3*b 6.1.1. b*b=b^2 b*b=b^(1+1) 6.1.1.1. 1+1=2 +1 _1_ 2 6.1.2. b^2*b=b^3 b^2*b=b^(2+1) 6.1.2.1. 2+1=3 +2 _1_ 3 6.1.3. b^3*b=b^4 b^3*b=b^(3+1) 6.1.3.1. 3+1=4 +3 _1_ 4 7. 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-(a^2*3+10*a*b+b^2*7) 7.1. (a+b)*(3*a+7*b)=a^2*3+10*a*b+b^2*7 (a+b)*(3*a+7*b)=a*3*a+a*7*b+b*3*a+b*7*b 7.1.1. a*a=a^2 a*a=a^(1+1) 7.1.1.1. 1+1=2 +1 _1_ 2 7.1.2. a*7*b+b*3*a=10*a*b 7.1.3. b*b=b^2 b*b=b^(1+1) 7.1.3.1. 1+1=2 +1 _1_ 2 8. 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-a^2*3-10*a*b-b^2*7 8.1. 3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-(a^2*3+10*a*b+b^2*7)=3*a^6*b^2+10*a^5*b^3+8*a^4*b^4-a^2*3-10*a*b-b^2*7

[latex]\frac{18a^4b+60a^3b^2+48a^2b^3}{6a^2b}-(a+b)(3a+7b)=[/latex] [latex]=\frac{18a^4b}{6a^2b}+\frac{60a^3b^2}{6a^2b}+\frac{48a^2b^3}{6a^2b}-(3a^2+7ab+3ab+7b^2)=[/latex] [latex]=3a^2+10ab+8b^2-3a^2-10ab-7b^2=b^2[/latex]