Advanced MathVery hardUsing a difference of squares to find a sum
Advanced Math practice question
If x² − y² = 40 and x − y = 4, what is the value of x + y?
Answer: 10
x² − y² = (x − y)(x + y). So 40 = 4(x + y), giving x + y = 10. (Here x = 7 and y = 3.)
Common wrong answers
- If you answered 36
- 36 is 40 − 4, subtracting instead of using the factored form (x − y)(x + y).
- If you answered 44
- 44 is 40 + 4. The relationship is multiplicative: 4 × (x + y) = 40.
- If you answered 160
- 160 is 40 × 4, multiplying instead of dividing.
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.