Advanced MathVery hardWhich expression equals a given difference for every x
Advanced Math practice question
For every value of x, which expression is equal to (x + 2)² − (x − 2)²?
- A. 8xCorrect
- B. 0
- C. 4x
- D. 2x² + 8
Answer: A. 8x
(x² + 4x + 4) − (x² − 4x + 4) = 8x. Or (a − b)(a + b) with a − b = 4 and a + b = 2x.
Why the other answers are wrong
- B. 0
- The two squares differ unless x = 0.
- C. 4x
- 4x halves the answer; the middle terms are +4x and −4x, giving 8x.
- D. 2x² + 8
- 2x² + 8 is the SUM of the two squares.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.