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Sagot :
Answer:
STEP
1
:
Equation at the end of step 1
(2ab•(c2))
(((((((3•(a2))•b)•c)+((a•(b2))•c))-——————————)-b2)+4bc)-4c
32a2
STEP
2
:
Equation at the end of step
2
:
2abc2
(((((((3•(a2))•b)•c)+((a•(b2))•c))-—————)-b2)+4bc)-4c
32a2
STEP
3
:
2abc2
Simplify —————
32a2
Dividing exponential expressions :
3.1 a1 divided by a2 = a(1 - 2) = a(-1) = 1/a1 = 1/a
Equation at the end of step
3
:
2bc2
(((((((3•(a2))•b)•c)+((a•(b2))•c))-————)-b2)+4bc)-4c
9a
STEP
4
:
Equation at the end of step
4
:
2bc2
((((((3a2•b)•c)+ab2c)-————)-b2)+4bc)-4c
9a
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 9a as the denominator :
3a2bc + ab2c (3a2bc + ab2c) • 9a
3a2bc + ab2c = ———————————— = ———————————————————
1 9a
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
6
:
Pulling out like terms
6.1 Pull out like factors :
3a2bc + ab2c = abc • (3a + b)
Adding fractions that have a common denominator :
6.2 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:
abc • (3a+b) • 9a - (2bc2) 27a3bc + 9a2b2c - 2bc2
—————————————————————————— = ——————————————————————
9a 9a
Equation at the end of step
6
:
(27a3bc + 9a2b2c - 2bc2)
((———————————————————————— - b2) + 4bc) - 4c
9a
STEP
7
:
Rewriting the whole as an Equivalent Fraction :
7.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 9a as the denominator :
b2 b2 • 9a
b2 = —— = ———————
1 9a
STEP
8
:
Pulling out like terms :
8.1 Pull out like factors :
27a3bc + 9a2b2c - 2bc2 = bc • (27a3 + 9a2b - 2c)
Trying to factor a multi variable polynomial :
8.2 Factoring 27a3 + 9a2b - 2c
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Adding fractions that have a common denominator :
8.3 Adding up the two equivalent fractions
bc • (27a3+9a2b-2c) - (b2 • 9a) 27a3bc + 9a2b2c - 9ab2 - 2bc2
——————————————————————————————— = —————————————————————————————
9a 9a
Equation at the end of step
8
:
(27a3bc + 9a2b2c - 9ab2 - 2bc2)
(——————————————————————————————— + 4bc) - 4c
9a
STEP
9
:
Rewriting the whole as an Equivalent Fraction :
9.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 9a as the denominator :
4bc 4bc • 9a
4bc = ——— = ————————
1 9a
STEP
10
:
Pulling out like terms :
10.1 Pull out like factors :
27a3bc + 9a2b2c - 9ab2 - 2bc2 =
b • (27a3c + 9a2bc - 9ab - 2c2)
Checking for a perfect cube :
10.2 27a3c + 9a2bc - 9ab - 2c2 is not a perfect cube
Adding fractions that have a common denominator :
10.3 Adding up the two equivalent fractions
b • (27a3c+9a2bc-9ab-2c2) + 4bc • 9a 27a3bc + 9a2b2c - 9ab2 + 36abc - 2bc2
———————————————————————————————————— = —————————————————————————————————————
9a 9a
Equation at the end of step
10
:
(27a3bc + 9a2b2c - 9ab2 + 36abc - 2bc2)
——————————————————————————————————————— - 4c
9a
STEP
11
:
Rewriting the whole as an Equivalent Fraction :
11.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 9a as the denominator :
4c 4c • 9a
4c = —— = ———————
1 9a
STEP
12
:
Pulling out like terms :
12.1 Pull out like factors :
27a3bc + 9a2b2c - 9ab2 + 36abc - 2bc2 =
b • (27a3c + 9a2bc - 9ab + 36ac - 2c2)
Adding fractions that have a common denominator :
12.2 Adding up the two equivalent fractions
b • (27a3c+9a2bc-9ab+36ac-2c2) - (4c • 9a) 27a3bc + 9a2b2c - 9ab2 + 36abc - 36ac - 2bc2
—————————————————————————————————————————— = ————————————————————————————————————————————
9a 9a
Trying to factor by pulling out :
12.3 Factoring: 27a3bc + 9a2b2c - 9ab2 + 36abc - 36ac - 2bc2
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 9a2b2c + 27a3bc
Group 2: 36abc - 36ac
Group 3: -9ab2 - 2bc2
Pull out from each group separately :
Group 1: (3a + b) • (9a2bc)
Group 2: (b - 1) • (36ac)
Group 3: (9ab + 2c2) • (-b)
Looking for common sub-expressions :
Group 1: (3a + b) • (9a2bc)
Group 3: (9ab + 2c2) • (-b)
Group 2: (b - 1) • (36ac)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Final result :
27a3bc + 9a2b2c + 9ab2 + 36abc + 36ac + 2bc2
————————————————————————————————————————————
9a
Answer:
=abc−a+2b−3c−4
Let's simplify step-by-step ;
2abc+3b−4c−7−(a+b−c+2)+5−abc
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