(x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)2•(x-3)2
Step-by-step explanation: Step by Step Solution
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STEP
1
:
Equation at the end of step 1
x-4)•(x-1)•(x+2))•(x+3))•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
2
:
Equation at the end of step 2
x-4)•(x-1)•(x+2)•(x+3))•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
3
:
Equation at the end of step 3
x-4)•(x-1)•(x+2)•(x+3)•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
4
:
Multiplying Exponential Expressions:
4.1 Multiply (x-4) by (x-4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-4) and the exponents are :
1 , as (x-4) is the same number as (x-4)1
and 1 , as (x-4) is the same number as (x-4)1
The product is therefore, (x-4)(1+1) = (x-4)2
Equation at the end of step
4
:
x-4)2•(x-1)•(x+2)•(x+3)•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
5
:
5.1 Rewrite (1-x) as (-1) • (x-1)
Multiplying Exponential Expressions:
5.2 Multiply (x-1) by (x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-1) and the exponents are :
1 , as (x-1) is the same number as (x-1)1
and 1 , as (x-1) is the same number as (x-1)1
The product is therefore, (x-1)(1+1) = (x-1)2
STEP
7
:
Pulling out like terms
7.1 Pull out like factors :
-x - 2 = -1 • (x + 2)
Multiplying Exponential Expressions:
7.2 Multiply (x + 2) by (x + 2)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+2) and the exponents are :
1 , as (x+2) is the same number as (x+2)1
and 1 , as (x+2) is the same number as (x+2)1
The product is therefore, (x+2)(1+1) = (x+2)2
STEP
9
:
Pulling out like terms
9.1 Pull out like factors :
-x - 3 = -1 • (x + 3)
Multiplying Exponential Expressions:
9.2 Multiply (x + 3) by (x + 3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as (x+3)1
and 1 , as (x+3) is the same number as (x+3)1
The product is therefore, (x+3)(1+1) = (x+3)
x-4)2•(x-1)2•(x+2)2•-1•(x+3)2•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
10
:
Equation at the end of step 10
x-4)2•(x-1)2•(x+2)2•(x+3)2•(-x-4)•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
11
:
STEP
12
:
Pulling out like terms
12.1 Pull out like factors :
-x - 4 = -1 • (x + 4)
Equation at the end of step
12
:
x-4)2•(x-1)2•(x+2)2•(x+3)2•(-x-4)•(x+1)•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)
STEP
13
:
STEP
14
:
Pulling out like terms
14.1 Pull out like factors :
-x - 4 = -1 • (x + 4)
Equation at the end of step
14
STEP
15
STEP
16
:
Pulling out like terms
16.1 Pull out like factors :
-x - 4 = -1 •
Equation at the end of step
16
:
STEP
17
:
STEP
18
:
Pulling out like terms
18.1 Pull out like factors :
-x - 4 = -1 • (x + 4)
Multiplying Exponential Expressions:
18.2 Multiply (x + 4) by (x + 4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
Equation at the end of step
18
:
(((x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(-x-1)•(2-x)•(3-x)•(x+1))•(2-x))•(x-3)
STEP
19
:
STEP
20
:
Pulling out like terms
20.1 Pull out like factors :
-x - 1 = -1 • (x + 1)
Multiplying Exponential Expressions:
20.2 Multiply (x + 1) by (x + 1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+1) and the exponents are :
1 , as (x+1) is the same number as (x+1)1
and 1 , as (x+1) is the same number as (x+1)1
The product is therefore, (x+1)(1+1) = (x+1)2
Equation at the end of step
20
:
((x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)•(3-x)•(2-x))•(x-3)
STEP
21
:
21.1 Rewrite (2-x) as (-1) • (x-2)
Multiplying Exponential Expressions:
21.2 Multiply (x-2) by (x-2)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-2) and the exponents are :
1 , as (x-2) is the same number as (x-2)1
and 1 , as (x-2) is the same number as (x-2)1
The product is therefore, (x-2)(1+1) = (x-2)2
22.1 Multiply (x-3) by (x-3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-3) and the exponents are :
1 , as (x-3) is the same number as (x-3)1
and 1 , as (x-3) is the same number as (x-3)1
The product is therefore, (x-3)(1+1) = (x-3)2
Final result :
(x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)2•(x-3)2
