a3b-2(ab-b2a)

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.

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.

Rewrite using the commutative property of multiplication.

a3b-22a⋅a-b⋅b2ab

Multiply a by a by adding the exponents.

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.

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.

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

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

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.

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

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.

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))