The product-sum technique, also known as the AC method or the decomposition method, is a strategy used to factor quadratic trinomials. It involves finding two numbers that multiply to he product of the leading coefficient and the constant term and add up to the coefficient of the linear term.

Here’s how it works:

1. Identify the Coefficients:
   Identify the values of a, b, and c
2. Find the Product and Sum: Calculate the product of a and $c,$and then find two numbers that multiply to ac and add up to b
3. Rewrite the Middle Term: Rewrite the middle term of the quadratic trinomial using the two numbers found in the previous step. This effectively splits the middle term into two terms.
4. Factor by Grouping: Group the first two terms together and the last two terms together. Factor out the greatest common factor from each group.
5. Factor Further: If possible, factor the expression obtained in the previous step.
6. Check: Verify that your factored expression matches the original quadratic trinomial.

This method is particularly useful when the quadratic trinomial cannot be factored easily by other techniques like trial and error or factoring by grouping alone. It’s a pretty systematic approach that can help efficiently factor most easy quadratic expressions.