Advanced MathHardDifference of two squared binomials
Advanced Math practice question
Which expression is equivalent to (x + y)² − (x − y)²?
- A. 4xyCorrect
- B. 2x² + 2y²
- C. 2xy
- D. 0
Answer: A. 4xy
(x + y)² = x² + 2xy + y² and (x − y)² = x² − 2xy + y². Subtracting: the x² and y² terms cancel, leaving 2xy − (−2xy) = 4xy.
Why the other answers are wrong
- B. 2x² + 2y²
- 2x² + 2y² is the SUM of the two squares. Subtracting cancels those terms instead.
- C. 2xy
- The cross terms are +2xy and −2xy; subtracting the second from the first gives 4xy, not 2xy.
- D. 0
- The two squares are different expressions, so their difference isn't zero (try x = 1, y = 1: 4 − 0 = 4).
More Advanced Math questions
- Hard
A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af… - Hard
How many real solutions does x² + 4x + 5 = 0 have? - Hard
A car worth $20,000 loses 15% of its value each year. What is its value after 2 years? - Hard
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye… - Hard
If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))? - Hard
The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?
Not affiliated with the College Board. SAT is a trademark of the College Board.