Factor: 36x^2 + 84xy + 49y^2.

1. Check that the first and last terms are perfect squares: 36x squared is (6x) squared, and 49y squared is (7y) squared. 2. Check the middle term: twice the product of 6x and 7y is 84xy, which matches. 3. Since all checks pass, write the square of the binomial: (6x + 7y)(6x + 7y). 4. Check by multiplying: 36x squared + 42xy + 42xy + 49y squared gives back 36x squared + 84xy + 49y squared. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_