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Chapter 0: Problem 16

Find each product. $$(x+5)\left(x^{2}-5 x+25\right)$$

Short Answer

Expert verified
The product of the given expression is \(x^{3} + 125\).

Step by step solution

01

Expand the Expression

Start by multiplying each term in the first bracket (binomial) by each term in the second bracket (trinomial). This is done as follows: \[x(x^{2}) + x(-5x) + x(25) + 5(x^{2}) + 5(-5x) + 5(25)\]
02

Simplify and Combine Like Terms

Now, simplify the expanded expression and combine those terms that have the same variable or exponent. Doing this, you get \[x^{3} - 5x^{2} + 25x + 5x^{2} - 25x + 125\] After combining like terms, this simplifies to: \[x^{3} + 125\]

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