(5ab^2+ab+b^2)*(2ba^2-ab+5)
Answers
Answer:
(2a2b + 1) • (2a2b - 1)
———————————————————————
2ab
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
b
(((2•(a2))•b)•a)-(5•————————)
(2•5ab2)
STEP
2
:
b
Simplify ————————
(2•5ab2)
Dividing exponential expressions :
2.1 b1 divided by b2 = b(1 - 2) = b(-1) = 1/b1 = 1/b
Equation at the end of step
2
:
1
(((2•(a2))•b)•a)-(5•————)
10ab
STEP
3
:
Equation at the end of step
3
:
1
((2a2 • b) • a) - ———
2ab
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2ab as the denominator :
2a3b 2a3b • 2ab
2a3b = ———— = ——————————
1 2ab
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 :
4.2 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:
2a3b • 2ab - (1) 4a4b2 - 1
———————————————— = —————————
2ab 2ab
Trying to factor as a Difference of Squares:
4.3 Factoring: 4a4b2 - 1
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 : 4 is the square of 2
Check : 1 is the square of 1
Check : a4 is the square of a2
Check : b2 is the square of b1
Factorization is : (2a2b + 1) • (2a2b - 1)
Trying to factor as a Difference of Squares:
4.4 Factoring: 2a2b - 1
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares