Pascal's Triangle: Binomial Expansion

Posljednje ažuriranje about 5 years ago

Pascal's Triangle: Binomial Expansion

Posljednje ažuriranje about 5 years ago

Complete the cells of Pascal's Triangle

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (a + b)⁵

Write out the complete term and include your calculations for determining the coefficient for:
6th term in the expansion of (c + d)⁸

Write out the complete term and include your calculations for determining the coefficient for:
2nd term in the expansion of (e + f)⁵

Write out the complete term and include your calculations for determining the coefficient for:
1st term in the expansion of (g + h)⁵

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (j + k)⁹

Write out the complete term and include your calculations for determining the coefficient for:
3rd term in the expansion of (m + n)⁴

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(a + b)⁴ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(c + d)⁷ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(e + f)⁵ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(g + h)⁶ =

What is the coefficient of the term a⁵b³ in (a + b)⁸? Include work/explanation for how you arrived at your answer.

What is the coefficient of the term a⁴b⁶ in (a + b)¹⁰? Include work/explanation for how you arrived at your answer.

Pascal's Triangle: Binomial Expansion

Pascal's Triangle: Binomial Expansion

Complete the cells of Pascal's Triangle

Write out the complete term and include your calculations for determining the coefficient for:5th term in the expansion of (a + b)5

5th term in the expansion of (a + b)5

Write out the complete term and include your calculations for determining the coefficient for:6th term in the expansion of (c + d)8

6th term in the expansion of (c + d)8

Write out the complete term and include your calculations for determining the coefficient for:2nd term in the expansion of (e + f)5

2nd term in the expansion of (e + f)5

Write out the complete term and include your calculations for determining the coefficient for:1st term in the expansion of (g + h)5

1st term in the expansion of (g + h)5

Write out the complete term and include your calculations for determining the coefficient for:5th term in the expansion of (j + k)9

5th term in the expansion of (j + k)9

Write out the complete term and include your calculations for determining the coefficient for:3rd term in the expansion of (m + n)4

3rd term in the expansion of (m + n)4

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(a + b)4 =

(a + b)4 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(c + d)7 =

(c + d)7 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(e + f)5 =

(e + f)5 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(g + h)6 =

(g + h)6 =

What is the coefficient of the term a5b3 in (a + b)8? Include work/explanation for how you arrived at your answer.

What is the coefficient of the term a4b6 in (a + b)10? Include work/explanation for how you arrived at your answer.

Complete the cells of Pascal's Triangle

Write out the complete term and include your calculations for determining the coefficient for:5th term in the expansion of (a + b)5

5th term in the expansion of (a + b)5

Write out the complete term and include your calculations for determining the coefficient for:6th term in the expansion of (c + d)8

6th term in the expansion of (c + d)8

Write out the complete term and include your calculations for determining the coefficient for:2nd term in the expansion of (e + f)5

2nd term in the expansion of (e + f)5

Write out the complete term and include your calculations for determining the coefficient for:1st term in the expansion of (g + h)5

1st term in the expansion of (g + h)5

Write out the complete term and include your calculations for determining the coefficient for:5th term in the expansion of (j + k)9

5th term in the expansion of (j + k)9

Write out the complete term and include your calculations for determining the coefficient for:3rd term in the expansion of (m + n)4

3rd term in the expansion of (m + n)4

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(a + b)4 =

(a + b)4 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(c + d)7 =

(c + d)7 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(e + f)5 =

(e + f)5 =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.(g + h)6 =

(g + h)6 =

What is the coefficient of the term a5b3 in (a + b)8? Include work/explanation for how you arrived at your answer.

What is the coefficient of the term a4b6 in (a + b)10? Include work/explanation for how you arrived at your answer.

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (a + b)⁵

5th term in the expansion of (a + b)⁵

Write out the complete term and include your calculations for determining the coefficient for:
6th term in the expansion of (c + d)⁸

6th term in the expansion of (c + d)⁸

Write out the complete term and include your calculations for determining the coefficient for:
2nd term in the expansion of (e + f)⁵

2nd term in the expansion of (e + f)⁵

Write out the complete term and include your calculations for determining the coefficient for:
1st term in the expansion of (g + h)⁵

1st term in the expansion of (g + h)⁵

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (j + k)⁹

5th term in the expansion of (j + k)⁹

Write out the complete term and include your calculations for determining the coefficient for:
3rd term in the expansion of (m + n)⁴

3rd term in the expansion of (m + n)⁴

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(a + b)⁴ =

(a + b)⁴ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(c + d)⁷ =

(c + d)⁷ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(e + f)⁵ =

(e + f)⁵ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(g + h)⁶ =

(g + h)⁶ =

What is the coefficient of the term a⁵b³ in (a + b)⁸? Include work/explanation for how you arrived at your answer.

What is the coefficient of the term a⁴b⁶ in (a + b)¹⁰? Include work/explanation for how you arrived at your answer.

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (a + b)⁵

5th term in the expansion of (a + b)⁵

Write out the complete term and include your calculations for determining the coefficient for:
6th term in the expansion of (c + d)⁸

6th term in the expansion of (c + d)⁸

Write out the complete term and include your calculations for determining the coefficient for:
2nd term in the expansion of (e + f)⁵

2nd term in the expansion of (e + f)⁵

Write out the complete term and include your calculations for determining the coefficient for:
1st term in the expansion of (g + h)⁵

1st term in the expansion of (g + h)⁵

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (j + k)⁹

5th term in the expansion of (j + k)⁹

Write out the complete term and include your calculations for determining the coefficient for:
3rd term in the expansion of (m + n)⁴

3rd term in the expansion of (m + n)⁴

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(a + b)⁴ =

(a + b)⁴ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(c + d)⁷ =

(c + d)⁷ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(e + f)⁵ =

(e + f)⁵ =

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(g + h)⁶ =

(g + h)⁶ =

What is the coefficient of the term a⁵b³ in (a + b)⁸? Include work/explanation for how you arrived at your answer.

What is the coefficient of the term a⁴b⁶ in (a + b)¹⁰? Include work/explanation for how you arrived at your answer.