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5.2 The Binomial Expansion
Name:
1. Without expanding (x + y)12, determine each of the following.
b) the value of k in the term xky7
a) the number of terms in the expansion
2. Use Pascal’s triangle to expand each of the following.
a) (3y – x)4
b) (2m3 + 4n-3)4
c) (5 – 2d)4
3. Write the first three terms of each expansion.
a) (x – 3y)21
c) (x + 3x1)6
b) (4x2 – y)11
4. Find the middle term in the expansion (2x – 3y)12.
5. The first four numbers in the row n = 90 of Pascal’s triangle are 1, 90, 4005, and 129 495.
a) Write the first four coefficients in the expansion of (x + y)90.
b) Write the last three coefficients in the row n = 90 of Pascal’s triangle.
c) Write the last four terms of the expansion of (x + y)90.
1 

6. Find the 21st term in the expansion  4 x  x 2 




24
.
7. a) Write x6 + 18x4 + 135x2 + 540 + 1215x2 + 1458x4 + 729x6
in the form (x + y)n.
5.2 The Binomial Expansion
Name:
1. Without expanding (x + y)12, determine each of the following.
d) the value of k in the term xky7
c) the number of terms in the expansion
2. Use Pascal’s triangle to expand each of the following.
d) (3y – x)4
e) (2m3 + 4n-3)4
f) (5 – 2d)4
3. Write the first three terms of each expansion.
d) (x – 3y)21
f) (x + 3x1)6
e) (4x2 – y)11
4. Find the middle term in the expansion (2x – 3y)12.
5. The first four numbers in the row n = 90 of Pascal’s triangle are 1, 90, 4005, and 129 495.
a) Write the first four coefficients in the expansion of (x + y)90.
b) Write the last three coefficients in the row n = 90 of Pascal’s triangle.
c) Write the last four terms of the expansion of (x + y)90.
1 


6. Find the 21st term in the expansion 4 x  x 2 




24
.
7. a) Write x6 + 18x4 + 135x2 + 540 + 1215x2 + 1458x4 + 729x6
in the form (x + y)n.