Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 2 more similar replacement(s).
(2): Dot was discarded near "a.(".
Step by step solution :
Step 1 : (0+(3•(a2)))-((((((a•(a-1)•(a+1))•(a+3))•(a2+1))•(a-3))•(a2-3))•(a+1))
Step 2 : (0+(3•(a2)))-(((((a•(a-1)•(a+1)•(a+3))•(a2+1))•(a-3))•(a2-3))•(a+1))
Step 3 : (0+(3•(a2)))-((((a•(a-1)•(a+1)•(a+3)•(a2+1))•(a-3))•(a2-3))•(a+1))
Step 4 :Polynomial Roots Calculator :Find roots (zeroes) of : F(a) = a2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 2.00 1 1 1.00 2.00
Polynomial Roots Calculator found no rational rootsstep 4 : (0+(3•(a2)))-(((a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3))•(a2-3))•(a+1))
step 5 : (0+(3•(a2)))-((a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3)•(a2-3))•(a+1))
Step 6 :Trying to factor as a Difference of Squares :Factoring: a2-3
(Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B) )
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
(Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.)
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
step 6 : (0+(3•(a2)))-(a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3)•(a2-3)•(a+1))
Step 7 :Evaluate an expression :Multiply (a+1) by (a+1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (a+1) and the exponents are :
1 , as (a+1) is the same number as (a+1)1
and 1 , as (a+1) is the same number as (a+1)1
The product is therefore, (a+1)(1+1) = (a+1)2
step 7 : (0+(3•(a2)))-a•(a-1)•(a+1)2•(a+3)•(a2+1)•(a-3)•(a2-3)
Step 8 : (0+3a2)-a•(a-1)•(a+1)2•(a+3)•(a2+1)•(a-3)•(a2-3)
Step 9 : Evaluate : (a+1)2 = a2+2a+1
Step 10 :Pulling out like terms : Pull out like factors :
-a10 - a9 + 12a8 + 12a7 - 26a6 - 26a5 - 12a4 - 12a3 + 30a2 + 27a =
-a • (a9 + a8 - 12a7 - 12a6 + 26a5 + 26a4 + 12a3 + 12a2 - 30a - 27)
Final result : -a • (a9 + a8 - 12a7 - 12a6 + 26a5 + 26a4 + 12a3 + 12a2 - 30a - 27)
hoped this helped