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Exercises Polynomials and factoring

Example 6.12 from Elementary Algebra, 6.1 Add and Subtract Polynomials

Add and Subtract Polynomials: example 6.12

Simplify: $(a^{3} - a^{2} b) - (a b^{2} + b^{3}) + (a^{2} b + a b^{2})$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

$(a^{3} - a^{2} b) - (a b^{2} + b^{3}) + (a^{2} b + a b^{2})$

Distribute. $a^{3} - a^{2} b - a b^{2} - b^{3} + a^{2} b + a b^{2}$

Rearrange the terms, to put like terms together. $a^{3} - a^{2} b + a^{2} b - a b^{2} + a b^{2} - b^{3}$

Combine like terms. $a^{3} - b^{3}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $(x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2})$ .

How did it go?

PreviousAdd and Subtract Polynomials: example 6.11 Next Add and Subtract Polynomials: example 6.13

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 6.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.