A difference of squares has two squared terms separated by subtraction. Rewrite each term as a square, then use one minus factor and one plus factor. You can graph the original and your product in Desmos to check that they overlap. Two minus factors instead change the constant and create a middle term.
Hints
- Hint 1
A perfect square is a quantity multiplied by itself. Rewrite both and as squares. What pattern do you see when one square is subtracted from the other?
- Hint 2
For a difference of squares, the factors use opposite signs so their middle terms cancel. A Desmos graph can check whether your product matches the original at every input, not just at one point.
Step-by-step
Spot the difference of squares
Step 1Rewrite the two squares
Since and , rewrite the expression:
This is a difference of squares: two squares with subtraction between them. Use one minus factor and one plus factor so the middle terms cancel.
- Step 2
Graph the original expression
Type in Desmos, using in place of to graph it. Click the vertex, the graph’s lowest point. Desmos labels it , confirming that the expression equals at . Any matching product must keep that constant value.
- Step 3
Check the matching product
Use and , the quantities you squared in step 1. Add in Desmos. It lies exactly on the original graph: the opposite-signed middle terms cancel, leaving for every . So the equivalent expression is . Choice D.