Algebraic Identities

Question 1

What is the formula for expanding (a + b)^2?

Answer 1

(a + b)^2 = a^2 + 2ab + b^2

Question 2

True or False: The expansion of (a + b)^2 involves three terms.

Answer 2

True

Question 3

Fill in the blank: The coefficient of the middle term in the expansion of (a + b)^2 is ____.

Answer 3

2

Question 4

What is the first term in the expansion of (a + b)^2?

Answer 4

a^2

Question 5

What is the last term in the expansion of (a + b)^2?

Answer 5

b^2

Question 6

In the expansion of (a + b)^2, what does the term 2ab represent?

Answer 6

The product of a and b, multiplied by 2.

Question 7

Multiple Choice: Which of the following is the correct expansion of (a + b)^2?

Answer 7

a^2 + 2ab + b^2

Question 8

What type of polynomial is (a + b)^2?

Answer 8

A quadratic polynomial.

Question 9

True or False: The expansion of (a + b)^2 can be derived from the distributive property.

Answer 9

True

Question 10

What is the degree of the polynomial (a + b)^2?

Answer 10

2

Question 11

Fill in the blank: The expansion of (a + b)^2 can also be written as ____ + ____ + ____.

Answer 11

a^2, 2ab, b^2

Question 12

What is the relationship between (a + b)^2 and (a - b)^2?

Answer 12

They have different middle terms; (a - b)^2 = a^2 - 2ab + b^2.

Question 13

Multiple Choice: Which term represents the interaction between a and b in the expansion of (a + b)^2?

Answer 13

2ab

Question 14

True or False: In the expansion of (a + b)^2, both a and b are squared.

Answer 14

True

Question 15

What happens to the sign of the middle term in the expansion of (a - b)^2 compared to (a + b)^2?

Answer 15

It becomes negative.

Question 16

What is the expanded form of (x + 3)^2?

Answer 16

x^2 + 6x + 9

Question 17

True or False: The expansion of (a + b)^2 is symmetric with respect to a and b.

Answer 17

True

Question 18

What is the second term in the expansion (a + b)^2?

Answer 18

2ab

Question 19

Fill in the blank: The expansion of (a + b)^2 results in a polynomial of ____ terms.

Answer 19

Three

Question 20

Multiple Choice: Which of the following is NOT a term in the expansion of (a + b)^2?

Answer 20

ab

Question 21

What is the expanded form of (2 + y)^2?

Answer 21

4 + 4y + y^2

Question 22

True or False: The expansion of (a + b)^2 can be visualized as the area of a square.

Answer 22

True

Question 23

What do the terms a^2 and b^2 represent in the expansion of (a + b)^2?

Answer 23

The areas of the squares formed by sides a and b.

Question 24

Fill in the blank: The expansion of (a + b)^2 is an example of ____ algebra.

Answer 24

binomial