DDesmos SAT Prep
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Checking Equivalent Expressions

Confirm two algebraic expressions are identical by graphing, not expanding.

The Desmos trick

Graph both expressions as separate functions — if their graphs sit exactly on top of each other (only one curve is visible), they're equivalent for every x. Even faster: graph expression1 minus expression2 and check that it's the flat line y = 0.

  • Graph y1 = (first expression) and y2 = (second expression) and look for a single visible curve
  • Fastest check: graph y = (expression 1) - (expression 2); if it's the flat line y = 0, they're equivalent
  • Great for testing 'which choice is equivalent to...' answer options one at a time

Practice questions

Q1Which expression is equivalent to (x + 3)^2 - 9?
Easy
Q2Which expression is equivalent to (2x - 1)(x + 4)?
Medium
Q3For which value of k is 3(x + 2) + 5 equivalent to 3x + k for all x?
Medium
Q4Which expression is equivalent to (x^2 - 9)/(x - 3) for x ≠ 3?
Hard
Q5If (x + a)^2 + b is equivalent to x^2 + 8x + 10 for all x, what is the…
Hard