Final answer:
To factor the perfect square trinomial 9x² -42x+49, identify it as a pattern (ax) ² - 2abx + b², then factor it as (3x - 7)² by following the steps provided.
Step-by-step explanation:
To factor the perfect square trinomial 9x² -42x+49, we can start by identifying a pattern that matches the form (ax) ² - 2abx + b², which factors to (ax - b)². In our case, consider 9x² as (3x)² and 49 as 7² with -42x representing -2(3x)(7). This leads us to the conclusion that our given expression is a perfect square trinomial that factors to:
(3x - 7)².
Step-by-step explanation:
- Identify the square root of the first term, which is 3x.
- Identify the square root of the last term, which is 7.
- Recognize that the middle term, -42x, should be twice the product of the square roots of the first and last terms with a negative sign, which it is (-2 * 3x * 7).
- Factor the trinomial as the square of a binomial: (3x - 7)².