Question

factor: 49p squared-14p+1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To factor the expression 49p^2 - 14p + 1, we can use the factoring method known as "grouping":

1. Multiply the coefficient of the quadratic term (49) by the constant term (1): 49 * 1 = 49.
2. Find two numbers that multiply to give 49 (the result of the previous step) and add up to the coefficient of the linear term (-14). In this case, those numbers are -7 and -7 since -7 * -7 = 49 and -7 + (-7) = -14.
3. Rewrite the middle term (-14p) using the numbers found in the previous step:
49p^2 - 7p - 7p + 1
4. Group the terms by pairs and factor out the greatest common factor from each pair:
(49p^2 - 7p) + (-7p + 1)
7p(7p - 1) - 1(7p - 1)
5. Notice that there is a common binomial factor (7p - 1) in both terms. Factor it out:
(7p - 1)(7p - 1)
Or, we can write it as:
(7p - 1)^2

Therefore, the factored form of 49p^2 - 14p + 1 is (7p - 1)^2.