Extra Practice: Binomial Expressions and Pascal's Triangle

1

If you want to find the 4th term in the expanded form of (x + y)14 without having a copy of Pascal's Triangle handy, what could you do mathematically to determine the coefficient?

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What would the full 4th term of (x + y)14 look like?

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Write out the other term in the expanded form of (x + y)14 that also has the same coefficient as your answer to question #2.

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In the expanded form of (m + n)15, which term has the greater coefficient: _?_m4n11 or _?_m7n8

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How could you determine your answer to question #4 without doing any calculations for the coefficients?

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Which of these two binomial expressions, when written in expanded form, will have only one maximum coefficient?

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Explain how you can determine the answer to question #6 without having to actually expand the binomial expressions.

2

Write out the complete term and include your calculations for determining the coefficient for:
9th term of (c + d)13

2

Write out the complete term and include your calculations for determining the coefficient for:
3rd term of (g + h)18

2

Write out the complete term and include your calculations for determining the coefficient for:
16th term of (y + z)19

2

If you want to find the 4th term in the expanded form of (x + y)14 without having a copy of Pascal's Triangle handy, what could you do mathematically to determine the coefficient?

What would the full 4th term of (x + y)14 look like?

Write out the other term in the expanded form of (x + y)14 that also has the same coefficient as your answer to question #2.

In the expanded form of (m + n)15, which term has the greater coefficient: _?_m4n11 or _?_m7n8

How could you determine your answer to question #4 without doing any calculations for the coefficients?

Which of these two binomial expressions, when written in expanded form, will have only one maximum coefficient?

Explain how you can determine the answer to question #6 without having to actually expand the binomial expressions.

Write out the complete term and include your calculations for determining the coefficient for:
9th term of (c + d)13

9th term of (c + d)13

Write out the complete term and include your calculations for determining the coefficient for:
3rd term of (g + h)18

3rd term of (g + h)18

Write out the complete term and include your calculations for determining the coefficient for:
16th term of (y + z)19

16th term of (y + z)19

Write out the complete term and include your calculations for determining the coefficient for:
20th term of (j + k)24

20th term of (j + k)24

Extra Practice: Binomial Expressions and Pascal's Triangle

If you want to find the 4th term in the expanded form of (x + y)14 without having a copy of Pascal's Triangle handy, what could you do mathematically to determine the coefficient?

What would the full 4th term of (x + y)14 look like?

Write out the other term in the expanded form of (x + y)14 that also has the same coefficient as your answer to question #2.

In the expanded form of (m + n)15, which term has the greater coefficient: _?_m4n11 or _?_m7n8

How could you determine your answer to question #4 without doing any calculations for the coefficients?

Which of these two binomial expressions, when written in expanded form, will have only one maximum coefficient?

Explain how you can determine the answer to question #6 without having to actually expand the binomial expressions.

Write out the complete term and include your calculations for determining the coefficient for:9th term of (c + d)13

9th term of (c + d)13

Write out the complete term and include your calculations for determining the coefficient for:3rd term of (g + h)18

3rd term of (g + h)18

Write out the complete term and include your calculations for determining the coefficient for:16th term of (y + z)19

16th term of (y + z)19

Write out the complete term and include your calculations for determining the coefficient for:20th term of (j + k)24

20th term of (j + k)24

Write out the complete term and include your calculations for determining the coefficient for:
9th term of (c + d)13

Write out the complete term and include your calculations for determining the coefficient for:
3rd term of (g + h)18

Write out the complete term and include your calculations for determining the coefficient for:
16th term of (y + z)19

Write out the complete term and include your calculations for determining the coefficient for:
20th term of (j + k)24