Question 1

Expand and simplify the following expression: $$(x^2 - 4y^3)^2$$

Accepted Answer

$$x^4 - 8x^2y^3 + 16y^6$$

Question 2

Which of the following is the correct application of the binomial square formula to $$(a - b)^2$$?

Accepted Answer

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

Question 3

If $$(3x - 2y)^2 is $$expanded, what is the coefficient of the $$xy$$ term?

Accepted Answer

$$-12$$

Question 4

Which of the following expressions is equivalent to $$(x^2 - 4y^3)^2$$?

Accepted Answer

$$(x^2)^2 - 2x^2 \cdot 4y^3 + (4y^3)^2$$

Question 5

A rectangular garden has a length of $$x^2$$ meters and a width of $$4y^3$$ meters. What is the area of two such gardens combined?

Accepted Answer

$$2x^2 \cdot 4y^3 = 8x^2y^3$$

Question 6

Which of the following is the result of squaring the binomial $$(2x - 5)^2$$?

Accepted Answer

$$4x^2 - 20x + 25$$

Question 7

If $$(a - b)^2 = 49 - 42 + 9$$, what are the values of $$a$$ and $$b$$?

Accepted Answer

$$a = 7, b = 3$$

Question 8

Which of the following is a common error when expanding $$(x^2 - 4y^3)^2$$?

Accepted Answer

$$x^4 - 16y^6$$

Question 9

A company’s profit is modeled by $$(x^2 - 4y^3)^2$$, where $$x is $$the number of products sold and $$y is $$the cost per product. If $$x = 2$$ and $$y = 1$$, what is the profit?

Accepted Answer

$$0$$

Question 10

Which of the following best describes the degree of the polynomial resulting from $$(x^2 - 4y^3)^2$$?

Accepted Answer

6

Expanding Binomial Expressions with Exponents

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