Question

How do you factor `9t^2+42t+49`?

Answer 1

`9t^2+42t+49 = (3t+7)^2`

Explanation:

This is a perfect square trinomial.

Notice that `9t^2 = (3t)^2` and `49 = 7^2` are both perfect squares, so it remains to check whether the middle term is correct:

`(3t+7)^2 = (3t)^2+2(3t)(7)+7^2 = 9t^2+42t+49`