Final answer:
The quadratic expression 25a² - 70a + 49 factors to (5a - 7)², which is a perfect square trinomial.
Step-by-step explanation:
The student has asked to factor the quadratic expression 25a² - 70a + 49.
To factor this, we need to find two numbers that multiply to the constant term (49) and add up to the coefficient of the linear term (-70).
Observing the expression, we can see that it is a perfect square trinomial because (5a)² = 25a², (7)² = 49, and
2(5a)(7) = 70a.
Therefore, the factored form of the quadratic is (5a - 7)².