SAT考试9月每日精选题30

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Mathematics>Standard Multiple Choice

Read the following sat test question and thenclick on a button to select your answer.

Which of the following expressions is equivalent to 16x^4-81?

A.(4x^3-9)(4x+9)

B.(2x-3)(2x+3)(4x^2-9)

C.(2x-3)(2x+3)(4x^2+9)

D.(2x-3)^4

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答案：C

解析：

A quick look at the answer choices tells us that we will want to factor the given expression.

Recall that a difference of squares of the form a^2-b^2 factors to (a-b)(a+b).

Because 16x^4 and 81 are both perfect squares, the expression 16x^4-81 is a difference of squares and can be factored as follows: 16x^4-81=(4x^2-9)(4x^2+9)

Note that the binomial(4x^2-9) also is a difference of squares. Therefore, we can continue our factorization as follows: (4x^2-9)(4x^2+9)=(2x-3)(2x+3)(4x^2+9)

16x^4-81 is equivalent to: (2x-3)(2x+3)(4x^2+9)

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