For problems #1-8 expand each expression fully.
1. \((x+4)^3\)
2. \((2x+1)^4\)
3. \((3x+5)^5\)
4. \((x+y)^4\)
5. \((a-3b)^3\)
6. \((r+w^2)^3\)
7. \((4x-3y)^5\)
8. \((a+b)^9\)
9. Find the 7th term in the expansion of \((5x-3)^{11}\).
10. Find the 18th term in the expansion of \((x-y)^{24}\).
11. Find the term in the expansion of \((5x-1)^7\) that contains \(x^3\).
12. Find the coefficient on \(x^3 y^8\) in the expansion of \((2x+5y)^{11}\).
13. The following is an image of Pascal's Triangle, which your teacher may have mentioned as a tool to compute binomial expansions. If you read each row of the triangle as a number you notice that the numbers are the powers of \(11\). Explain how you know this is not a coincidence.
Hint: \(11=\left(10+1\right)\)
1. \((x+4)^3\)
2. \((2x+1)^4\)
3. \((3x+5)^5\)
4. \((x+y)^4\)
5. \((a-3b)^3\)
6. \((r+w^2)^3\)
7. \((4x-3y)^5\)
8. \((a+b)^9\)
9. Find the 7th term in the expansion of \((5x-3)^{11}\).
10. Find the 18th term in the expansion of \((x-y)^{24}\).
11. Find the term in the expansion of \((5x-1)^7\) that contains \(x^3\).
12. Find the coefficient on \(x^3 y^8\) in the expansion of \((2x+5y)^{11}\).
13. The following is an image of Pascal's Triangle, which your teacher may have mentioned as a tool to compute binomial expansions. If you read each row of the triangle as a number you notice that the numbers are the powers of \(11\). Explain how you know this is not a coincidence.
Hint: \(11=\left(10+1\right)\)
Review Problems
14. Determine a trigonometric function for the following graph.
15. Approximate the 48th term of a geometric sequence whose first term is \(3\) and common ratio is \(\large\frac{12}{11}\).
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