Same Math › Grades 7–9 › The box method in algebra
What is the box method in algebra?
The box method is the area model kids used for 23 × 14, now with x. To multiply (x + 3)(x + 2), write one factor across the top and one down the side, fill each box with a product, and add: x² + 3x + 2x + 6 = x² + 5x + 6. Run backwards, the same box factors expressions.
- Top and side: the two factors, split into terms.
- Each box: top × side.
- Add the boxes and combine like terms.
Why schools teach it
It replaces FOIL
Seventh graders expand expressions like 3(x + 4) (7.EE.A.1), and Algebra 1 students multiply and factor expressions like x² + 5x + 6 (HSA.SSE.A.2). Many of us learned FOIL (first, outer, inner, last), which only works for two terms times two terms.
The box works for any size and organizes every product, so nothing gets missed. Factoring becomes filling in a box whose total you already know.
At the kitchen table
What to say, and what to skip
Say this
What goes across the top and down the side?
What's top times side in this box?
Which boxes are like terms?
Usually the diagonal ones.To factor: which two numbers multiply to the last term and add to the middle?
Skip this
Just use FOIL.
FOIL fails for bigger expressions. The box always works.- Dropping negative signs.Write −2 as its own term in the header, sign included.
- Forgetting to combine like terms.3x and 2x in separate boxes add to 5x.
See it in action
Factoring x² + 7x + 12
Put x² in the top-left box and 12 in the bottom-right
Find two numbers that multiply to 12 and add to 7
3 and 4Read the factors off the top and side
(x + 3)(x + 4)
Check by multiplying the factors back with the box.
Free practice sheet
Make a box method sheet
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Parents also ask
Is this the same as the area model for numbers?
Yes. 23 × 14 split into tens and ones uses exactly the same grid.
What's wrong with FOIL?
Nothing for two terms times two terms. The box works for every size, so it's taught instead.
What grade is factoring?
Usually Algebra 1, in eighth or ninth grade. Distributing with a box starts in sixth or seventh.
What about negative numbers?
Put the sign in the header: (x − 2) becomes x and −2. Then multiply signs as usual.