FACTOR:
36x^2+132xy+121y^2
since 36 and 121 are both perfect squares, my first guess would be
(6x+11y)^2
Sure enough, 132 = 2*6*11.
To factor the expression 36x^2 + 132xy + 121y^2, we can use the factoring method called "perfect square trinomial."
A perfect square trinomial is a trinomial that can be factored into two identical binomials. The binomials will have the same terms but with opposite signs.
In this case, the given expression 36x^2 + 132xy + 121y^2 has a similar structure to (ax + by)^2. By comparing the given expression with the perfect square trinomial, we can determine the values of a and b.
If we break down the expression 36x^2 + 132xy + 121y^2, we can see that:
- The first term is the square of 6x: (6x)^2 = 36x^2
- The last term is the square of 11y: (11y)^2 = 121y^2
- The middle term is 2 * 6x * 11y = 132xy.
Therefore, we can write the expression as (6x + 11y)^2.
In conclusion, the factored form of 36x^2 + 132xy + 121y^2 is (6x + 11y)^2.