Understanding and applying the binomial theorem

which number is a coefficient found in the eighth row?

• 36

• 70

• 284

• 5

• 1452

Expand the binomial using Pascal's Triangle.

• A

• B

• C

• D

True or False:
The coefficients of the 3rd and the 7th terms in the expansion of

 $\left(x+y\right)^8$  are identical.

• True

• False

If you expand (x + 1)⁶ using the binomial theorem, which describes BEST what you do?

• You multiply (x + 1) by itself 6 times

• You use patterns with exponents and pascal's triangle row 6 to find the answer.

• You use the numbers from row 6 of Pascal's triangle to write 7 terms.

• You distribute the exponent of 6.

According to Pascal's triangle, you would multiply the fourth term of the 8th degree binomial expansion by the number __________.

Tags

AII.9-12.7.B

P.9-12.5.F

What is row 7 of Pascal's Triangle?

• 1, 5, 10, 5, 1

• 1, 5, 10, 10, 5, 1

• 1, 6, 15, 20, 15, 6, 1

• 1, 7, 21, 35, 21, 7, 1

How do you create Pascal's Triangle?

• The first row is all 1's, 2nd all 2's, third all 3's, etc.
• 1's all the way down on the outside of both right and left sides, then add the two numbers above each space to complete the triangle.
• Use the perfect square numbers
• Count by twos

Dakota said the third term of the expansion of (2g + 3h)^4 is 36g^2h^2. Explain Dakota’s error. Then correct the error.

• Dakota's error is in the value of the variables

• Dakota's error is in the calculation of the third term

• Dakota's error is in the binomial expansion formula

• Dakota's error is in the value of the coefficients

If the top row of Pascal's Triangle is row 0, then what is the sum of the numbers in the eighth row?

• 255

• 256

• 257

• 260

• 264

What is row 5 of Pascal's Triangle?

• 1, 2, 1
• 1, 3, 3, 1
• 1, 4, 9, 4, 1
• 1, 5, 10, 10, 5, 1