Question
21. \( (3 c-8)^{2} \)
Ask by Barrett Montgomery. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 9c^{2} - 48c + 64 \)
Solution
To expand the expression \( (3c - 8)^2 \), you can use the formula for squaring a binomial:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Applying this formula to \( (3c - 8)^2 \):
\[
(3c - 8)^2 = (3c)^2 - 2 \times 3c \times 8 + 8^2
\]
Calculate each term:
1. **First term:** \((3c)^2 = 9c^2\)
2. **Second term:** \(-2 \times 3c \times 8 = -48c\)
3. **Third term:** \(8^2 = 64\)
Combine these results:
\[
(3c - 8)^2 = 9c^2 - 48c + 64
\]
**Final Answer:**
\( 9c^{2} - 48c + 64 \)
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Simplify this solution Bonus Knowledge
To expand \( (3c - 8)^{2} \), we use the binomial formula \((a - b)^{2} = a^{2} - 2ab + b^{2}\). Here, \(a = 3c\) and \(b = 8\). So, we get: - First term: \((3c)^{2} = 9c^{2}\) - Second term: \(-2(3c)(8) = -48c\) - Third term: \(8^{2} = 64\) Putting it all together, the expansion gives us: \[ (3c - 8)^{2} = 9c^{2} - 48c + 64 \]
