Read the following SAT test question and then click on a button to select your answer.
Which of the following expressions is equivalent to16x^4-81?
factor ['fæktə] n. 因素，因子
multiple ['mʌltipl] adj. 许多，多种多样的
equivalent [i'kwivələnt] adj. 等价的，相等的
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)