Question
Find the factors of \( x^{2}-64 \)
Ask by Ball Chang. in Sri Lanka
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factors of \( x^{2}-64 \) are \( (x-8) \) and \( (x+8) \).
Solution
1. Recognize that \( x^{2}-64 \) is a difference of two squares because it can be written as
\[
x^{2} - 8^{2}.
\]
2. The difference of two squares formula is given by
\[
a^{2} - b^{2} = (a-b)(a+b).
\]
3. In this case, \( a = x \) and \( b = 8 \). Substitute these values into the formula to get
\[
x^{2}-64 = (x-8)(x+8).
\]
Thus, the factors of \( x^{2}-64 \) are
\[
(x-8)(x+8).
\]
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Simplify this solution Mind Expander
The expression \( x^{2} - 64 \) is a difference of squares, which can be factored using the formula \( a^{2} - b^{2} = (a - b)(a + b) \). In this case, \( a = x \) and \( b = 8 \) (since \( 64 = 8^{2} \)). Therefore, the factors are \( (x - 8)(x + 8) \). Another way to think about it is to visualize it as cutting a square with side \( x \) and area \( x^{2} \) into two smaller squares, each with area 64, making it super easy to see how you get those neat little factors! So next time you're stumped, just remember: sometimes it's just a matter of recognizing patterns!
