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Chapter 0: Problem 32

Find each product. $$(x+5)(x-5)$$

Short Answer

Expert verified
The product of \((x+5)(x-5)\) simplifies to \(x^2 - 25.\)

Step by step solution

01

Apply the Distributive Property

Start by multiplying every term in the first binomial, \((x+5)\), with every term in the second binomial, \((x鈭�5)\). This can also be done by following the FOIL method, meaning that you first multiply the first terms in each binomial, then the outer terms, then the inner terms, and finally the last terms in each binomial. This gives us: \[ (x+5)(x-5) = x(x) + x(-5) + 5(x) + 5(-5) = x^2 - 5x + 5x - 25.\]
02

Combine Like Terms

Next, combine like terms \[ x^2 - 5x + 5x - 25 = x^2 + 0 - 25.\] The term \(- 5x + 5x\) simplifies to 0 because they are like terms (terms having same variable and power) and sum up to zero.
03

Simplify result

After combining the like terms, we need to simplify the result by skipping any addition or subtraction by zero. This will leave us with:\[ x^2 + 0 - 25 = x^2 - 25. \]Therefore, \((x+5)(x-5)\) simplifies to \(x^2 - 25\).

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