BackFactoring Special Products quiz
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1/15BackSkip to main contentBackWhat is the formula for factoring a difference of squares?
The formula is a^2 - b^2 = (a + b)(a - b). What criteria must be met to use the difference of squares factoring rule?
Both terms must be perfect squares and have opposite signs. How would you factor x^2 - 4 using the difference of squares rule?
It factors as (x + 2)(x - 2). Can a sum of squares, like a^2 + b^2, be factored using the difference of squares rule?
No, a sum of squares cannot be factored using this rule. How do you factor 16 - 9x^2 using the difference of squares?
It factors as (4 + 3x)(4 - 3x). What is a perfect square trinomial and how is it factored?
A perfect square trinomial has first and last terms as perfect squares and the middle term as 2ab; it factors as (a ± b)^2. How do you factor x^2 + 10x + 25 as a perfect square trinomial?
It factors as (x + 5)^2. What must the middle term of a perfect square trinomial equal for factoring?
The middle term must equal 2ab, where a and b are the square roots of the first and last terms. How do you factor 4x^2 - 36x + 81 as a perfect square trinomial?
It factors as (2x - 9)^2. What determines whether you use (a + b)^2 or (a - b)^2 when factoring a perfect square trinomial?
The sign of the middle term determines whether you use plus or minus. What is the formula for factoring a sum of cubes?
a^3 + b^3 = (a + b)(a^2 - ab + b^2). What is the formula for factoring a difference of cubes?
a^3 - b^3 = (a - b)(a^2 + ab + b^2). How do you factor x^3 + 8 using the sum of cubes rule?
It factors as (x + 2)(x^2 - 2x + 4). What does the SOAP acronym stand for in factoring cubes?
SOAP stands for Same, Opposite, Always Positive, describing the signs in the binomial and trinomial factors. How do you factor 27y^3 - 1 using the difference of cubes rule?
It factors as (3y - 1)(9y^2 + 3y + 1).
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