Use the structure of an expression to identify ways to rewrite it. For example see x⁴ - y⁴ as (x²)² - (y²)² and factor accordingly.

Sample Practice Questions (3)

A cube with side length

a

has a smaller cube with side length

2

removed from its corner. Which expression represents the remaining volume?

(a - 2) (a^{2} + 2 a + 4)

(a - 2)^{3}

(a + 2) (a^{2} - 2 a + 4)

a^{3} - 2

Which of the following is an equivalent form of

x^{2} + 10 x + 21

that reveals the vertex of the corresponding parabola?

(x + 5)^{2} - 4

(x + 5)^{2} + 4

(x + 10)^{2} - 79

(x + 3) (x + 7)

The graph of a quadratic function

f (x)

is shown below. Which of the following expressions represents the function in vertex form?

f (x) = (x - 3)^{2} - 4

f (x) = (x + 3)^{2} - 4

f (x) = (x - 3)^{2} + 4

f (x) = (x + 3)^{2} + 4

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