Problem 16

Question

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

Step-by-Step Solution

Verified
Answer
The product of the given expression is \(x^{3} + 125\).
1Step 1: 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: \[x(x^{2}) + x(-5x) + x(25) + 5(x^{2}) + 5(-5x) + 5(25)\]
2Step 2: 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: \[x^{3} + 125\]