How would 3x^2-27y^2 be factored completely?
isnt it the difference of two squares?
3(x^2-9y^2)=3(x-3y)*(x+3y)
Yes but isnt the difference of two squares just one technique to factor polynomials?
Of course. If one technique works to factor a polynomial, it is factored.
To factor the expression 3x^2 - 27y^2 completely, first, we need to factor out the greatest common factor (GCF) from both terms. In this case, the GCF is 3.
Step 1: Factor out the GCF:
3(x^2 - 9y^2)
At this point, we have a difference of squares in the parentheses, which can be factored further.
Step 2: Recognize the difference of squares:
3((x)^2 - (3y)^2)
The difference of squares can be written as (a^2 - b^2) = (a + b)(a - b), where "a" represents "x" and "b" represents "3y".
Step 3: Apply the difference of squares formula:
3(x + 3y)(x - 3y)
Therefore, the expression 3x^2 - 27y^2 can be factored completely as 3(x + 3y)(x - 3y).