Equivalent Expressions
The same expression can be written in different forms that are always equal, no matter what values you plug in. Adjust the sliders and watch the factored and expanded forms stay in sync.
Expanding means multiplying factors out into a sum of terms — FOIL (First, Outer, Inner, Last) is the standard way to expand two binomials. Factoring is the reverse: rewriting a sum of terms as a product. Both directions describe the exact same expression — they just look different.
A common shortcut worth memorizing: difference of squares, a² − b² = (a − b)(a + b). It shows up constantly in simplifying fractions and solving equations, since it lets you cancel a matching factor top and bottom.
On the SAT, these questions usually ask which of four expressions is equivalent to a given one — expand or factor whichever form is easier to work with, then match terms rather than trying to “see” the answer directly.