### 3ab^2-4a^3b+ab^2/4ab^2

This encounters reducing fountain to your lowest terms.

## Step by action Solution ## Step 1 :

b2 leveling —— 4 Equation at the end of action 1 : b2 ((3a•(b2))-((4•(a3))•b))+(((a•——)•a)•b2) 4

## step 2 :

Multiplying exponential expression :2.1 b2 multiply by b2 = b(2 + 2) = b4

Equation in ~ the end of action 2 :

a2b4 ((3a•(b2))-((4•(a3))•b))+———— 4

## step 3 :

Equation in ~ the finish of step 3 : a2b4 ((3a • (b2)) - (22a3 • b)) + ———— 4

## step 4 :

Equation in ~ the end of step 4 : a2b4 (3ab2 - 22a3b) + ———— 4

## Step 5 :

Rewriting the whole as an Equivalent portion :5.1Adding a fraction to a whole Rewrite the whole as a fraction using 4 as the denominator :

3ab2 - 4a3b (3ab2 - 4a3b) • 4 3ab2 - 4a3b = ——————————— = ————————————————— 1 4 Equivalent fraction : The fraction thus produced looks different yet has the same value together the whole typical denominator : The equivalent fraction and the other portion involved in the calculation share the exact same denominator

## Step 6 :

Pulling out like terms :

6.1 traction out prefer factors:3ab2 - 4a3b=-ab•(4a2 - 3b)

Trying to factor as a distinction of Squares:6.2 Factoring: 4a2 - 3b theory : A distinction of 2 perfect squares, A2-B2can it is in factored into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ abdominal muscle - B2 = A2 - B2Note : abdominal = BA is the commutative residential or commercial property of multiplication. Keep in mind : -AB+ ab equals zero and also is because of this eliminated from the expression.Check: 4 is the square the 2Check: 3 is no a square !! judgment : Binomial can not it is in factored as the difference of two perfect squares.

Adding fractions that have actually a usual denominator :6.3 including up the two tantamount fractions add the two equivalent fractions i m sorry now have a usual denominatorCombine the molecule together, placed the sum or distinction over the usual denominator then mitigate to lowest terms if possible:

-ab • (4a2-3b) • 4 + a2b4 -16a3b + a2b4 + 12ab2 ————————————————————————— = ————————————————————— 4 4

## Step 7 :

Pulling out choose terms :7.1 pull out choose factors:-16a3b + a2b4 + 12ab2=-ab•(16a2 - ab3 - 12b)

Trying to aspect a multi variable polynomial :7.2 Factoring16a2 - ab3 - 12bTry to aspect this multi-variable trinomial utilizing trial and also errorFactorization fails