Question 1

Which of the following correctly applies the FOIL method to $ (x + 2)(x + 3) $?

Accepted Answer

$ x^2 + 5x + 6 $

Question 2

What is the result of $ (x - 5)(x - 12) $ using the FOIL method?

Accepted Answer

$ x^2 - 17x + 60 $

Question 3

A chemist is mixing two solutions represented by $ (x - 3x)(2x + 8) $. What is the simplified product?

Accepted Answer

$ -4x^2 - 16x $

Question 4

Which of the following is the correct expansion of $ (x + 4)(3x^2 - 2x + 1) $?

Accepted Answer

$ 3x^3 + 10x^2 - 7x + 4 $

Question 5

A company models its profit with $ (x + 3)(x - 5)(-2x + 1) $. What is the expanded form?

Accepted Answer

$ -2x^3 + 8x^2 - 28x + 15 $

Question 6

Which formula represents the difference of squares for $ (a + b)(a - b) $?

Accepted Answer

$ a^2 - b^2 $

Question 7

What is the result of $ (5x - 9)(5x + 9) $ using the special product formula?

Accepted Answer

$ 25x^2 - 81 $

Question 8

Which of the following is the correct expansion for $ (3x + 5)(3x + 5) $?

Accepted Answer

$ 9x^2 + 30x + 25 $

Question 9

A cube-shaped container has a side length represented by $ (x - 3) $. What is the volume in expanded form?

Accepted Answer

$ x^3 - 9x^2 + 27x - 27 $

Question 10

Which formula correctly expands $ (a + b)^3 $?

Accepted Answer

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

Question 11

Expand $ (2x + 4)^3 $ using the cube formula.

Accepted Answer

$ 8x^3 + 48x^2 + 96x + 64 $

Question 12

A pharmaceutical company uses $ (x^2 - 2x)(x^2 + x - 2) $ to model a reaction. What is the expanded form?

Accepted Answer

$ x^4 - x^3 - 4x^2 + 4x $

Question 13

Which step is necessary when multiplying $ x(x^2 - 2) $?

Accepted Answer

Distribute $ x $ to each term in $ x^2 - 2 $

Question 14

Expand $ (x + 6)^2 $ using the perfect square trinomial formula.

Accepted Answer

$ x^2 + 12x + 36 $

Question 15

A biologist models population growth with $ (x + 7)(-x + 6) $. What is the expanded form?

Accepted Answer

$ -x^2 + 6x - 7x + 42 $

Question 16

Which of the following is the correct expansion for $ (x^2 + 3x - 2)(x^2 + x - 2) $?

Accepted Answer

$ x^4 + 4x^3 - 7x^2 - 8x + 4 $

Question 17

Which property allows you to multiply $ x^2(x - 2) $ as $ x^3 - 2x^2 $?

Accepted Answer

Distributive Property

Question 18

Expand $ (x + 2)^2 $ using the perfect square trinomial formula.

Accepted Answer

$ x^2 + 4x + 4 $

Question 19

A student multiplies $ (x + 3)^2 $ and gets $ x^2 + 9 $. What mistake did they make?

Accepted Answer

They forgot to include the $ 2ab $ term in the expansion.

Multiplying Polynomials: FOIL Method and Special Products

Study Guide - Practice Questions