Question 1

Which of the following correctly represents the expansion of $$ (a+b)^2$ $$?

Accepted Answer

$$ a^2$ + 2ab + b^2$ $$

Question 2

Given $$ (a-b)^2$ $$, which of the following is the correct expansion?

Accepted Answer

$$ a^2$ - 2ab + b^2$ $$

Question 3

What is the result of factoring $$ a^2$ - b^2$ $$?

Accepted Answer

$$ (a+b)(a-b) $$

Question 4

Which expression is equivalent to $$ (a+b)^3$ $$?

Accepted Answer

$$ a^3$ + 3a^2$b + 3ab^2$ + b^3$ $$

Question 5

If $$ (a-b)^3$  is $$expanded, which of the following is the correct result?

Accepted Answer

$$ a^3$ - 3a^2$b + 3ab^2$ - b^3$ $$

Question 6

Which of the following is the correct factorization for $$ a^3$ + b^3$ $$?

Accepted Answer

$$ (a+b)(a^2$-ab+b^2$$) $

Question 7

Which of the following is the correct factorization for $$ a^3$ - b^3$ $$?

Accepted Answer

$$ (a-b)(a^2$+ab+b^2$$) $

Question 8

A pharmaceutical company needs to calculate the volume of a cube-shaped container. If the side length is $$ (a+b) $$, what is the volume?

Accepted Answer

$$ (a+b)^3$ $$

Question 9

Which of the following expressions represents the difference of cubes?

Accepted Answer

$$ a^3$ - b^3$ $$

Question 10

If you are given $$ x^2$ + 2xy + y^2$ $$, which factoring method should you use?

Accepted Answer

Perfect square trinomial

Question 11

A rectangular garden has sides $$ a $$ and $$ b . If $$you want to build a path around it such that the new sides are $$ (a+b) $$, what is the area of the new garden?

Accepted Answer

$$ (a+b)^2$ $$

Question 12

Which of the following is the correct expansion for $$ (a+b)^2$  in $$terms of real-world applications, such as calculating the area of a square with side $$ (a+b) $$?

Accepted Answer

$$ a^2$ + 2ab + b^2$ $$

Question 13

If $$ a = 2 $$ and $$ b = 3 $$, what is the value of $$ (a+b)^3$ $$?

Accepted Answer

Question 14

Which of the following is NOT a valid factoring method for $$ a^2$ - b^2$ $$?

Accepted Answer

$$ (a^2$-b^2$$) $

Question 15

A company wants to design a box with a volume given by $$ (a-b)^3$ . $$Which of the following is the correct expansion for the volume?

Accepted Answer

$$ a^3$ - 3a^2$b + 3ab^2$ - b^3$ $$

Question 16

Which of the following is the correct expansion for $$ (a-b)^2$ $$?

Accepted Answer

$$ a^2$ - 2ab + b^2$ $$

Question 17

If $$ a = 4 $$ and $$ b = 2 $$, what is the value of $$ a^2$ - b^2$ $$?

Accepted Answer

$$ 12 $$

Question 18

Which of the following is the correct factorization for $$ a^3$ - b^3$ $$?

Accepted Answer

$$ (a-b)(a^2$+ab+b^2$$) $

Question 19

If $$ a = 1 $$ and $$ b = 2 $$, what is the value of $$ (a+b)^2$ $$?

Accepted Answer

$$ 4 $$

Question 20

Which of the following is the correct expansion for $$ (a+b)^3$ $$?

Accepted Answer

$$ a^3$ + 3a^2$b + 3ab^2$ + b^3$ $$

Precalculus: Algebraic Expressions, Factoring, and Polynomial Expansion

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