find the product of
Answers
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
3 2 (2•(b2)) q
((—•b)+——)•((————————+————)-1)
2 3b 4 32b2
STEP
2
:
q
Simplify ————
32b2
Equation at the end of step
2
:
3 2 (2•(b2)) q
((—•b)+——)•((————————+———)-1)
2 3b 4 9b2
STEP
3
:
Equation at the end of step
3
:
3 2 2b2 q
((—•b)+——)•((———+———)-1)
2 3b 4 9b2
STEP
4
:
2b2
Simplify ———
4
Dividing exponents:
4.1 21 divided by 22 = 2(1 - 2) = 2(-1) = 1/21 = 1/2
Equation at the end of step
4
:
3 2 b2 q
((—•b)+——)•((——+———)-1)
6.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 18b2 as the denominator :
1 1 • 18b2
1 = — = ————————
1 18b2
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
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
(9b4+2q) - (18b2) 9b4 - 18b2 + 2q
————————————————— = ———————————————
18b2 18b2
Equation at the end of step
6
:
3 2 (9b4-18b2+2q)
((—•b)+——)•—————————————
2 3b 18b2
STEP
7
:
2
Simplify ——
3b
Equation at the end of step
7
:
3 2 (9b4 - 18b2 + 2q)
((— • b) + ——) • —————————————————
2 3b 18b2
STEP
8
:
3
Simplify —
2
Equation at the end of step
8
:
3 2 (9b4 - 18b2 + 2q)
((— • b) + ——) • —————————————————
2 3b 18b2
STEP
9
:
Calculating the Least Common Multiple :
9.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 3b
2 3b 2 9b2
Equation at the end of step
5
:
3 2 (9b4+2q)
((—•b)+——)•(————————-1)
2 3b 18b2
Equation at the end of step
9
:
(9b2 + 4) (9b4 - 18b2 + 2q)
————————— • —————————————————
6b 18b2
STEP
10
:
Polynomial Roots Calculator :
10.1 Find roots (zeroes) of : F(b) = 9b2+4
Polynomial Roots Calculator is a set of methods aimed at finding values of b for which F(b)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers b 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 9 and the Trailing Constant is 4.
The factor(s) are:
of the Leading Coefficient : 1,3 ,9
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 13.00
-1 3 -0.33 5.00
-1 9 -0.11 4.11
-2 1 -2.00 40.00
-2 3 -0.67 8.00
Note - For tidiness, printing of 13 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Trying to factor a multi variable polynomial :
10.2 Factoring 9b4 - 18b2 + 2q
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Multiplying exponential expressions :
10.3 b1 multiplied by b2 = b(1 + 2) = b3
Final result :
(9b2 + 4) • (9b4 + 18b2 + 2q)
—————————————————————————————
108b3