1Cademy - Simplifying $$(a^3 - a^2b) - (ab^2 + b^3) + (a^2b + ab^2)$$

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Adding and Subtracting Polynomials

Example

Simplifying $(a^3 - a^2b) - (ab^2 + b^3) + (a^2b + ab^2)$

To simplify the polynomial expression $(a^3 - a^2b) - (ab^2 + b^3) + (a^2b + ab^2)$ , first distribute the negative sign to the second polynomial, which changes the sign of each of its terms: $a^3 - a^2b - ab^2 - b^3 + a^2b + ab^2$ . Next, rewrite the expression without the parentheses, rearranging the terms to group like terms together: $a^3 - a^2b + a^2b - ab^2 + ab^2 - b^3$ . Finally, combine the like terms. The $-a^2b$ and $+a^2b$ cancel each other out, as do the $-ab^2$ and $+ab^2$ , leaving the simplified result: $a^3 - b^3$ .