Объяснение: Для умножения многочлена на многочлен существует очень легкое правило. Чтобы умножить два многочлена между собой, надо каждый член первого многочлена умножить на каждый член второго многочлена. После это полученные произведения сложить и привести подобные.
2. А
Объяснение: У вырази a*b е два множники, ''a''*b називається першим множником, а*''b'' називається другим множником.
3. В
Объяснение: Спрощуючи даний вираз, згрупуємо окремо числові та буквені множники.
4. Г
5. Б
Объснение: Коэффицие́нт «совместно» + «производящий») — термин, обозначающий числовой множитель при буквенном выражении, множитель при той или иной степени неизвестного, или постоянный множитель при переменной величине.
-a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a) Reformatting the input :
Changes made to your input should not affect the solution:
(1): "c2" was replaced by "c^2". 2 more similar replacement(s).
Step by step solution :Skip Ad Step 1 : c2 Simplify ————— c - a Equation at the end of step 1 : (a2) (b2) c2 ((—————•(a-c))+(—————•(b-a)))+(———•(c-b)) (a-b) (b-c) c-a Step 2 :Equation at the end of step 2 : (a2) (b2) c2•(c-b) ((—————•(a-c))+(—————•(b-a)))+———————— (a-b) (b-c) c-a Step 3 : b2 Simplify ————— b - c Equation at the end of step 3 : (a2) b2 c2•(c-b) ((—————•(a-c))+(———•(b-a)))+———————— (a-b) b-c c-a Step 4 :Equation at the end of step 4 : (a2) b2•(b-a) c2•(c-b) ((—————•(a-c))+————————)+———————— (a-b) b-c c-a Step 5 : a2 Simplify ————— a - b Equation at the end of step 5 : a2 b2•(b-a) c2•(c-b) ((———•(a-c))+————————)+———————— a-b b-c c-a Step 6 :Equation at the end of step 6 : a2•(a-c) b2•(b-a) c2•(c-b) (————————+————————)+———————— a-b b-c c-a Step 7 :Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : a-b
The right denominator is : b-c
Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} a-b 101 b-c 011
Least Common Multiple: (a-b) • (b-c)
Calculating Multipliers :
7.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = b-c
Right_M = L.C.M / R_Deno = a-b
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. a2 • (a-c) • (b-c) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) R. Mult. • R. Num. b2 • (b-a) • (a-b) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 ——————————————————————————————————————— = —————————————————————————————————————————— (a-b) • (b-c) (a - b) • (b - c) Equation at the end of step 7 : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) ———————————————————————————————————————————— + ———————————— (a - b) • (b - c) c - a Step 8 :Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : (a-b) • (b-c)
The right denominator is : c-a
Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} a-b 101 b-c 101 c-a 011
Least Common Multiple: (a-b) • (b-c) • (c-a)
Calculating Multipliers :
8.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = c-a
Right_M = L.C.M / R_Deno = (a-b)•(b-c)
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) —————————————————— = ———————————————————————————————————————— L.C.M (a-b) • (b-c) • (c-a) R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c) —————————————————— = —————————————————————————— L.C.M (a-b) • (b-c) • (c-a) Adding fractions that have a common denominator :
1. Б
Объяснение: Для умножения многочлена на многочлен существует очень легкое правило. Чтобы умножить два многочлена между собой, надо каждый член первого многочлена умножить на каждый член второго многочлена. После это полученные произведения сложить и привести подобные.
2. А
Объяснение: У вырази a*b е два множники, ''a''*b називається першим множником, а*''b'' називається другим множником.
3. В
Объяснение: Спрощуючи даний вираз, згрупуємо окремо числові та буквені множники.
4. Г
5. Б
Объснение: Коэффицие́нт «совместно» + «производящий») — термин, обозначающий числовой множитель при буквенном выражении, множитель при той или иной степени неизвестного, или постоянный множитель при переменной величине.
6. А
Changes made to your input should not affect the solution:
Step by step solution :Skip Ad(1): "c2" was replaced by "c^2". 2 more similar replacement(s).
Step 1 : c2 Simplify ————— c - a Equation at the end of step 1 : (a2) (b2) c2 ((—————•(a-c))+(—————•(b-a)))+(———•(c-b)) (a-b) (b-c) c-a Step 2 :Equation at the end of step 2 : (a2) (b2) c2•(c-b) ((—————•(a-c))+(—————•(b-a)))+———————— (a-b) (b-c) c-a Step 3 : b2 Simplify ————— b - c Equation at the end of step 3 : (a2) b2 c2•(c-b) ((—————•(a-c))+(———•(b-a)))+———————— (a-b) b-c c-a Step 4 :Equation at the end of step 4 : (a2) b2•(b-a) c2•(c-b) ((—————•(a-c))+————————)+———————— (a-b) b-c c-a Step 5 : a2 Simplify ————— a - b Equation at the end of step 5 : a2 b2•(b-a) c2•(c-b) ((———•(a-c))+————————)+———————— a-b b-c c-a Step 6 :Equation at the end of step 6 : a2•(a-c) b2•(b-a) c2•(c-b) (————————+————————)+———————— a-b b-c c-a Step 7 :Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
Number of times each Algebraic FactorThe left denominator is : a-b
The right denominator is : b-c
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a-b 101 b-c 011
Calculating Multipliers :Least Common Multiple:
(a-b) • (b-c)
7.2 Calculate multipliers for the two fractions
Making Equivalent Fractions :Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = b-c
Right_M = L.C.M / R_Deno = a-b
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. a2 • (a-c) • (b-c) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) R. Mult. • R. Num. b2 • (b-a) • (a-b) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) Adding fractions that have a common denominator :Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
7.4 Adding up the two equivalent fractions
a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 ——————————————————————————————————————— = —————————————————————————————————————————— (a-b) • (b-c) (a - b) • (b - c) Equation at the end of step 7 : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) ———————————————————————————————————————————— + ———————————— (a - b) • (b - c) c - a Step 8 :Calculating the Least Common Multiple :Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
8.1 Find the Least Common Multiple
Number of times each Algebraic FactorThe left denominator is : (a-b) • (b-c)
The right denominator is : c-a
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a-b 101 b-c 101 c-a 011
Calculating Multipliers :Least Common Multiple:
(a-b) • (b-c) • (c-a)
8.2 Calculate multipliers for the two fractions
Making Equivalent Fractions :Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = c-a
Right_M = L.C.M / R_Deno = (a-b)•(b-c)
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) —————————————————— = ———————————————————————————————————————— L.C.M (a-b) • (b-c) • (c-a) R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c) —————————————————— = —————————————————————————— L.C.M (a-b) • (b-c) • (c-a) Adding fractions that have a common denominator :8.4 Adding up the two equivalent fractions
(a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) + c2 • (c-b) • (a-b) • (b-c) -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————— = ————————————————————————————————————————————————————————————————————————————————————————————— (a-b) • (b-c) • (c-a) (a-b) • (b-c) • (c-a) Final result : -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a)
Latest drills solved(-4,7)to(94,-55)(5)/(7)+(4)/(y)=38(x+8/9)-9a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b)Processing ends successfully