Question

Factoring:::
p^2 - 2p +1
(p+1) (p + 1 )
x^2 - 2xy - 48y^2
(x-8y) (x+6y)
a^2 + 4ab - 45b^2
(a -9b) this one is a factor of the whole problem only
just checking my work

Answer 1

p^2 -2p +1 does not equal (p+1)(p+1)
(p+1)(p+1) = p^2 +2p + 1

Answer 2

Remember that the signs have to match. To check your work when factoring, multiply the factors back out and see if they match. In the first problem:
(p+1)(p+1) = p^2 + 2p + 1, not p^2 - 2p + 1

Answer 3

first one is (p-1)(p-1)

Answer 4

second is right.

Answer 5

third is (a+9b)(a-5b)

Answer 6

The solution to the last one is (a+9b)(a-5b)

Remember that this problem is generally of the form (ax + by)(cx + dy) = (ac)x^2 + (ad+bc)xy + (bd)y^2, so when you solve the problem plug the numbers in and make sure they work.

For example, -45 = either -15*3, 15*-3 or -9*5, or 9*-5. Since we know the coefficients of both a's are 1, that means that the (ad+bc) part of the general form simplifies to 4=(b+d), the two factors of -45. Only 1 of the above pairs of numbers adds up to 4