For all real values of a and b, what is the simplified form of the expression 3a^3b - 2ab^… — ACT

For all real values of $a$ and $b$ , what is the simplified form of the expression $3a^3b - 2ab^2 - (a^3b - 5ab^2)$ ?

2a^3b + 3ab^2

The correct expression is found by distributing the negative sign across the parentheses to change the signs of the terms inside, yielding

-a^3b + 5ab^2

. Combining the like terms

3a^3b

and

-a^3b

gives

2a^3b

, and combining

-2ab^2

and

+5ab^2

gives

3ab^2

Distribute the negative sign to each term inside the parenthetical expression:

-(a^3b - 5ab^2)

-a^3b + 5ab^2

To remove the parentheses, we multiply each term inside by

-1

Rewrite the full expression with the parentheses removed:

3a^3b - 2ab^2 - a^3b + 5ab^2

3a^3b - 2ab^2 - a^3b + 5ab^2

This sets up the expression for combining like terms.

Group and combine the like terms:

(3a^3b - a^3b)

and

(-2ab^2 + 5ab^2)

2a^3b + 3ab^2

Only terms with the exact same variable parts and exponents can be combined by adding or subtracting their coefficients.

Simplifying algebraic expressions by distributing negative signs and combining like terms.

Estimated Time:45s

Question