Factor completely.16t2–56t+49

Sure, here are the steps to factor the given expression completely:

1. The given expression is 16t^2 - 56t + 49.

2. First, we look for the greatest common factor (GCF). In this case, the GCF is 1.

3. Next, we look at the expression in the form of ax^2 + bx + c. We need to find two numbers that multiply to give ac (which is 16*49 = 784) and add up to give b (which is -56).

4. The two numbers that satisfy these conditions are -28 and -28 because -28*-28 = 784 and -28 + -28 = -56.

5. We rewrite the middle term of the expression as the sum of the products of these two numbers and the variable t. So, the expression becomes 16t^2 - 28t - 28t + 49.

6. Now, we group the terms to factor by grouping: (16t^2 - 28t) - (28t - 49).

7. We factor out the GCF from each group: 4t(4t - 7) - 7(4t - 7).

8. Now, we notice that (4t - 7) is a common factor in both terms, so we factor that out to get: (4t - 7)(4t - 7).

9. Since (4t - 7)(4t - 7) is the same as (4t - 7)^2, the completely factored form of the expression is (4t - 7)^2.