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Chapter 5: Problem 63

Find each product. $$(a+b)\left(a^{2}-b^{2}\right)$$

Short Answer

Expert verified
\[a^3-b^3\]

Step by step solution

01

Identify the binomial and difference of squares

For the multiplication (a+b)(a^2-b^2), (a+b) is the binomial, and \(a^2-b^2\) is the difference of squares.
02

Apply the distributive property part 1

Distribute the first term of the binomial, a, to the difference of squares which results in \(a(a^2-b^2)\) which simplifies to \(a^3-ab^2\).
03

Apply the distributive property part 2

Next, distribute the second term of the binomial, b, to the difference of squares which results in \(b(a^2-b^2)\). That simplifies to \(ab^2-b^3\).
04

Combine terms

Now, bring the results of the two distributions together. \(a^3-ab^2+ab^2-b^3\).
05

Final simplification

Simplify the expression by combining like terms. The simpler form is \(a^3-b^3\).

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