每日一题

Mathematics

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

答案和解析

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)