Polynomials & quadratics
Multiply polynomials
ALEKS placement
Every term in the first factor multiplies every term in the second.
What this covers
- Count the products you should get: terms times terms.
- Multiply coefficients and add exponents on each pairing.
- Write out all the products before combining anything.
- Combine like terms and order by descending power.
Worked example
Worked example
Multiply (2x + 3)(x² - x + 4).
- 2x3−2x2+8x+3x2−3x+12Six products: 2x against three terms, then 3 against three terms.
- 2x3+x2+5x+12Combine like terms.
Another worked example
Expand (2x − 3)(x + 4).
- 2x⋅x+2x⋅4−3⋅x−3⋅4Each term on the left multiplies each term on the right.
- 2x2+8x−3x−12Multiply coefficients and variable factors; the final constant is negative.
- 2x2+5x−12Only the two x terms combine.
A common mistake
A mistake Lemma catches
From 2x⋅x+2x⋅4−3⋅x−3⋅4
10x2−3x−122x2+8x−3x−12
“You combined 2x² and 8x into 10x², but they are not like terms — only terms with the same letter raised to the same power can be added together.”
Try one
Sample problem
Expand and simplify.
(x−1)(x−3)Practice polynomial products free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
Where this fits
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