Question
Multiply (x + 3)(x + 2) using the FOIL method.
Solution — Step by Step
FOIL is just a memory tool for multiplying two binomials — First, Outer, Inner, Last. Each letter tells you which pair of terms to multiply. We’ll multiply all four pairs and then combine.
The First terms are x (from the first bracket) and x (from the second bracket).
Outer means the terms on the far outside — x and +2.
Inner means the terms closest to each other in the middle — +3 and x.
Last terms are +3 and +2.
Now collect all four results: . Combine the like terms 2x and 3x:
Why This Works
When we multiply (x + 3)(x + 2), we’re really asking: “what is each term in the first bracket × each term in the second bracket?” The distributive property says (x + 3)(x + 2) = x(x + 2) + 3(x + 2). FOIL is just this distribution done in a neat, memorable order.
The 5x in the middle comes from adding the outer and inner products — 2x + 3x. This middle term is where students most often make errors, so it’s worth pausing here.
For any two binomials (x + a)(x + b), the middle term is always (a + b)x and the last term is always ab. So for (x + 3)(x + 2), the answer is x² + (3+2)x + (3×2) = x² + 5x + 6. Once you see this pattern, you can skip FOIL for simple cases and write the answer directly.
Alternative Method
We can use the standard distributive method (also called the “each-by-each” method), which is what FOIL actually is under the hood.
Treat (x + 2) as a single block and distribute (x + 3) over it:
Same answer, same steps — just written differently. This form is more useful when you move to multiplying a trinomial by a binomial later in Class 9-10.
Common Mistake
The most common error is forgetting the Outer and Inner steps — students multiply only First and Last, writing x² + 6 and missing the 5x entirely. This happens because x² and 6 feel like “the obvious parts.” Always ask: where is the middle term coming from? If your answer has no x term when multiplying two linear expressions, something went wrong.
Another frequent slip: writing x² + 2x + 3x + 6 correctly but then adding the like terms as x² + 5x² + 6, treating 5x as 5x². Keep track of the exponent — 2x + 3x = 5x, not 5x².