Simplify a/(3b)-2(a/b-b/(2a))

Math
a3b-2(ab-b2a)
Simplify each term.
Tap for more steps…
To write ab as a fraction with a common denominator, multiply by 2a2a.
a3b-2(ab⋅2a2a-b2a)
To write -b2a as a fraction with a common denominator, multiply by bb.
a3b-2(ab⋅2a2a-b2a⋅bb)
Write each expression with a common denominator of b⋅2a, by multiplying each by an appropriate factor of 1.
Tap for more steps…
Multiply ab and 2a2a.
a3b-2(a(2a)b(2a)-b2a⋅bb)
Multiply b2a and bb.
a3b-2(a(2a)b(2a)-b⋅b2ab)
Reorder the factors of b(2a).
a3b-2(a(2a)2ab-b⋅b2ab)
a3b-2(a(2a)2ab-b⋅b2ab)
Combine the numerators over the common denominator.
a3b-2a(2a)-b⋅b2ab
Simplify the numerator.
Tap for more steps…
Rewrite using the commutative property of multiplication.
a3b-22a⋅a-b⋅b2ab
Multiply a by a by adding the exponents.
Tap for more steps…
Move a.
a3b-22(a⋅a)-b⋅b2ab
Multiply a by a.
a3b-22a2-b⋅b2ab
a3b-22a2-b⋅b2ab
Multiply b by b by adding the exponents.
Tap for more steps…
Move b.
a3b-22a2-(b⋅b)2ab
Multiply b by b.
a3b-22a2-b22ab
a3b-22a2-b22ab
a3b-22a2-b22ab
Cancel the common factor of 2.
Tap for more steps…
Factor 2 out of -2.
a3b+2(-1)2a2-b22ab
Factor 2 out of 2ab.
a3b+2(-1)2a2-b22(ab)
Cancel the common factor.
a3b+2⋅-12a2-b22(ab)
Rewrite the expression.
a3b-12a2-b2ab
a3b-12a2-b2ab
Rewrite -12a2-b2ab as -2a2-b2ab.
a3b-2a2-b2ab
a3b-2a2-b2ab
To write a3b as a fraction with a common denominator, multiply by aa.
a3b⋅aa-2a2-b2ab
To write -2a2-b2ab as a fraction with a common denominator, multiply by 33.
a3b⋅aa-2a2-b2ab⋅33
Write each expression with a common denominator of 3ba, by multiplying each by an appropriate factor of 1.
Tap for more steps…
Multiply a3b and aa.
a⋅a3ba-2a2-b2ab⋅33
Multiply 2a2-b2ab and 33.
a⋅a3ba-(2a2-b2)⋅3ab⋅3
Reorder the factors of 3ba.
a⋅a3ab-(2a2-b2)⋅3ab⋅3
Reorder the factors of ab⋅3.
a⋅a3ab-(2a2-b2)⋅33ab
a⋅a3ab-(2a2-b2)⋅33ab
Combine the numerators over the common denominator.
a⋅a-(2a2-b2)⋅33ab
Simplify the numerator.
Tap for more steps…
Multiply a by a.
a2-(2a2-b2)⋅33ab
Apply the distributive property.
a2+(-(2a2)–b2)⋅33ab
Multiply 2 by -1.
a2+(-2a2–b2)⋅33ab
Multiply –b2.
Tap for more steps…
Multiply -1 by -1.
a2+(-2a2+1b2)⋅33ab
Multiply b2 by 1.
a2+(-2a2+b2)⋅33ab
a2+(-2a2+b2)⋅33ab
Apply the distributive property.
a2-2a2⋅3+b2⋅33ab
Multiply 3 by -2.
a2-6a2+b2⋅33ab
Move 3 to the left of b2.
a2-6a2+3⋅b23ab
Subtract 6a2 from a2.
-5a2+3b23ab
-5a2+3b23ab
Simplify with factoring out.
Tap for more steps…
Factor -1 out of -5a2.
-(5a2)+3b23ab
Factor -1 out of 3b2.
-(5a2)-(-3b2)3ab
Factor -1 out of -(5a2)-(-3b2).
-(5a2-3b2)3ab
Simplify the expression.
Tap for more steps…
Rewrite -(5a2-3b2) as -1(5a2-3b2).
-1(5a2-3b2)3ab
Move the negative in front of the fraction.
-5a2-3b23ab
-5a2-3b23ab
-5a2-3b23ab
Simplify a/(3b)-2(a/b-b/(2a))

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

Solve all your Math Problems: https://elanyachtselection.com/

We can solve all your math problems
Scroll to top