Problem 31
Question
Find each product. $$(x+3)(x-3)$$
Step-by-Step Solution
Verified Answer
The product of the binomials is \(x^2 - 9\).
1Step 1: Identify the pattern
Realize that \((x+3)(x-3)\) fits the form \((a + b)(a - b)\), where \(a = x\) and \(b = 3\).
2Step 2: Apply the difference of squares pattern
Use the pattern to simplify the expression. Therefore, \((a + b)(a - b)\) equals \(a^2 - b^2\). Substituting for values of \(a\) and \(b\) we get: \(x^2 - 3^2\).
3Step 3: Simplify the result
Perform the calculation in the expression obtained to get a final simplified answer, which will be: \(x^2 - 9\).
Other exercises in this chapter
Problem 31
Multiply or divide as indicated. $$\frac{x^{2}+x-12}{x^{2}+x-30} \cdot \frac{x^{2}+5 x+6}{x^{2}-2 x-3} \div \frac{x+3}{x^{2}+7 x+6}$$
View solution Problem 31
Factor each trinomial, or state that the trinomial is prime. $$ 9 x^{2}-9 x+2 $$
View solution Problem 31
Simplify each exponential expression in Exercises 23–64. $$\left(x^{3}\right)^{7}$$
View solution Problem 31
Find the union of the sets. \(\\{1,3,5,7\\} \cup\\{2,4,6,8,10\\}\)
View solution