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Guias de estudo > ALGEBRA / TRIG I

Summary: Factoring Special Cases

Key Concepts

Perfect Square Trinomials  A perfect square trinomial can be written as the square of a binomial:
a2+2ab+b2=(a+b)2{a}^{2}+2ab+{b}^{2}={\left(a+b\right)}^{2}
a2−2ab+b2=(a−b)2{a}^{2}-2ab+{b}^{2}={\left(a-b\right)}^{2}
How to factor a perfect square trinomial
  1. Confirm that the first and last term are perfect squares.
  2. Confirm that the middle term is twice the product of abab.
  3. Write the factored form as (a+b)2{\left(a+b\right)}^{2} or (a−b)2{\left(a-b\right)}^{2}.
Differences of Squares  A difference of squares can be rewritten as two factors containing the same terms but opposite signs.
a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)
The Sum of Cubes  A binomial in the form a3+b3a^{3}+b^{3} can be factored as (a+b)(a2–ab+b2)\left(a+b\right)\left(a^{2}–ab+b^{2}\right). The Difference of Cubes  A binomial in the form a3–b3a^{3}–b^{3} can be factored as (a−b)(a2+ab+b2)\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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