Question 1

Which of the following is the correct expansion of $$(x + 2)(x + 4)$$?

Accepted Answer

$$x^2 + 6x + 8$

Question 2

A rectangular garden has a length of $$(x + 2)$$ meters and a width of $$(x + 7)$$ meters. What is the area of the garden in terms of $$x$$?

Accepted Answer

$$x^2 + 9x + 14$

Question 3

Expand and simplify $$(2x + 1)(x - 5).$$

Accepted Answer

$$2x^2 - 9x - 5$

Question 4

Which of the following is the result of multiplying $$(k - 4)(k + 5)$$?

Accepted Answer

$$k^2 + k - 20$

Question 5

A company wants to build a rectangular billboard with a height of $$(3x + 1)$$ meters and a width of $$(3x + 2)$$ meters. What is the area of the billboard in terms of $$x$$?

Accepted Answer

$$9x^2 + 9x + 2$

Question 6

Expand and simplify $$(x + 4)^2$.

Accepted Answer

$$x^2 + 8x + 16$

Question 7

Which of the following expressions is equivalent to $$(2a + 5b)(a - 4b)$$?

Accepted Answer

$$2a^2 - 3ab$$ - $$20b^2$$

Question 8

Expand and simplify $$(x + 5)(x^2$ + 4x - 8).$$

Accepted Answer

$$x^3$$ + $$9x^2 + 12x - 40$

Question 9

Which of the following is the correct expansion of $$(4m + n)(m - 2n)$$?

Accepted Answer

$$4m^2 - 7mn$$ - $$2n^2$$

Question 10

A square plot of land has a side length of $$(p - 7)$$ meters. What is the area of the plot in terms of $$p$$?

Accepted Answer

$$p^2 - 14p + 49$

Question 11

Expand and simplify $$(3a + 4b)(3a - 4b).$$

Accepted Answer

$$9a^2$$ - $$16b^2$$

Question 12

Which of the following is the result of multiplying $$(2w + 1)(2w - 1)$$?

Accepted Answer

$$4w^2 - 1$

Question 13

Expand and simplify $$(k + 4)(3k + 2).$$

Accepted Answer

Question 14

Expand and simplify $$(x + 1)(x - 1).$$

Accepted Answer

$$x^2 - 1$

Question 15

A rectangular field has a length of $$(5x + 2)$$ meters and a width of $$(3x - 1)$$ meters. What is the area of the field in terms of $$x$$?

Accepted Answer

$$15x^2 + x - 2$

Question 16

Expand and simplify $$(2r + s)(2r - s).$$

Accepted Answer

Question 17

Which of the following is the correct expansion of $$(x + 4)(x^2$ + 3x - 6)$$?

Accepted Answer

$$x^3$$ + $$7x^2 + 6x - 24$

Question 18

Expand and simplify $$(a + 3b)^2$.

Accepted Answer

$$a^2 + 6ab$$ + $$9b^2$$

Question 19

A company is designing a square logo with side length $$(4m + 1)$$ centimeters. What is the area of the logo in terms of $$m$$?

Accepted Answer

$$16m^2 + 8m + 1$

Step-by-Step Guidance: Multiplying Binomials and Trinomials in College Algebra

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