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

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

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

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