Expanding Double Brackets
Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms
What a learner can do afterwards
- Expand the product of two binomials using a systematic method (grid or FOIL)
- Collect like terms after expansion to simplify the result
- Expand products involving negative terms correctly
1 · Read
You already know how to expand a single bracket. Now there are two brackets, each with two terms. Every term in the first bracket has to multiply every term in the second bracket. That gives four small multiplications in total.
Expand (x + 3)(x - 2). First terms: x times x makes x squared. Outer terms: x times -2 makes -2x. Inner terms: 3 times x makes 3x. Last terms: 3 times -2 makes -6. Written out, that is x squared - 2x + 3x - 6.
FOIL just names the order: First, Outer, Inner, Last. It helps you remember all four multiplications so you never miss one. Any order works, as long as every term meets every term. A squared bracket such as (x + 1)² is two brackets, (x + 1)(x + 1), so you expand it the same way.
Now collect like terms in x squared - 2x + 3x - 6. The -2x and 3x are like terms, so add them: -2x + 3x = x. The simplified answer is x squared + x - 6.
Watch the signs closely. In (x - 4)(x + 5): First is x squared, Outer is 5x, Inner is -4x, Last is -20. Collecting 5x - 4x gives x, so the answer is x squared + x - 20.
Multiply every term in the first bracket by every term in the second, then collect like terms to finish.
Readings 'Two brackets as a rectangle' and 'Negative terms in the brackets' are original to this dataset. 5 extra questions are original to this dataset. Extra question x3 follows the problem template poly_mult_sub_03 by Rick Lynch (University of Missouri-Columbia), WeBWorK Open Problem Library, licensed CC BY-NC-SA 3.0. Extra questions x5 and x6 follow the problem template poly_mult_sub_02 by Rick Lynch (University of Missouri-Columbia), WeBWorK Open Problem Library, licensed CC BY-NC-SA 3.0.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.