Which of the following expressions is not a factor of `16x^(4)-81y^(4)`?

Options

A. `2x-3y`
B. `2x+3y`
C. `4x-9y`
D. `4x^(2)+9y^(2)`

Answer

C

Explanation

Difficult: Medium
Category: Passport to Advanced Math/ Quadratics
Strategy Advice:Being able to rewrite an expression as an equivalent expression (for example, by factoring it ) will certainly earn you points on Test Day.
Getting to the Answer: Examine each of the terms in the expression as an equivalent: Each terms is a perfect square and the terms are joined by a minus sign, so the expression is a difference to two squares. Use the factoring rule `a^(2)-b^(2)=(a+b)(a-b)` to factor the expression:
`16x^(4)-81y^(4)=(4x^(2))^(2)-(9y^(2))^(2)=(4x^(2)-9y^(2))(4x^(2)-9y^(2))`
You can eliminate D because `(4x^(2)+9y^(2))` is one of the factor given. Next, notice that the second factor is another difference of two squares, so you can factor it further using the same rule:
`4x^(2)-9y^(2)-(2x)^(2)-(3y)^(2)=(2x-3y)(2x+3y)`
You can now eliminate A and B, leaving (C) as the expression that is not a factor of `16x^(4)-81y^(4)`.