Bluebook SAT Test Equivalent Expressions 15

Question 1

Which of the following is equivalent to (x + 2y)²?

Accepted Answer

x² + 4xy + 4y²

Answer

Using (a+b)²=a²+2ab+b²: a=x, b=2y → x²+2(x)(2y)+(2y)² = x²+4xy+4y².

Question 2

Which expression is equivalent to (x³ − x) / x?

Accepted Answer

x² − 1

Answer

Divide each term by x: x³/x = x², (−x)/x = −1; result is x²−1.

Question 3

Which of the following is equivalent to −4(x + 2)² + 4(x + 2)?

Accepted Answer

All of the above

Answer

Factor out 4(x+2): 4(x+2)[−(x+2)+1] = 4(x+2)(−x−1); this equals −4(x+2)(x+1), so all listed are equivalent.

Question 4

Which of the following is equivalent to (a²b − ab²) / ab?

Accepted Answer

a − b

Answer

Factor numerator: ab(a−b); divide by ab to get a−b.

Question 5

Which expression is equivalent to (5x − 4)(5x + 4)?

Accepted Answer

25x² − 16

Answer

Difference of squares: (5x)²−4² = 25x²−16.

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