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: \[x^{3} + 125\]
Other exercises in this chapter
Problem 16
Multiply or divide as indicated. $$\frac{6 x+9}{3 x-15} \cdot \frac{x-5}{4 x+6}$$
View solution Problem 16
$$\text { Factor by grouping.}$$ $$x^{3}-x^{2}-5 x+5$$
View solution Problem 16
Use the product rule to simplify the expressions in Exercises \(13-22\) In Exercises \(17-22,\) assume that variables represent nonnegative real Numbers. $$\sqr
View solution Problem 17
Evaluate each exponential expression. $$\frac{2^{8}}{2^{4}}$$
View solution