SOLUTION: Please help! How do I factor, if possible, the following? (a) y^2 + 16y + 64 (b) by + 7b - 6y - 42 How do I solve the following for the roots of each quadratic equati

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Question 71901This question is from textbook Beginning Algebra
: Please help!
How do I factor, if possible, the following?
(a) y^2 + 16y + 64
(b) by + 7b - 6y - 42
How do I solve the following for the roots of each quadratic equation?
(c) x^2 - x - 20 = 0
(d) 9x^2 = 81
I have been working on these problems for the past few hours, but can't seem to solve using the right formula. Maybe there is something I am doing wrong. This question is from textbook Beginning Algebra

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Factor:
(a) Notice that the first and last terms are perfect squares. This suggests the possibility that the expression itself may be a perfect square. Since , you can try:

Check using FOIL:
=
The factors are: and
(b) Here, you use use "factor by grouping". Group the terms as folows:
Notice the change of sign on the last term when the parentheses were added. Now, from each group, factor the common factors.
Now you can factor the common factor of (y+7)
These are the factors.
Solve:
(c) This will factor. Notice that the last term has factors of 4 and 5. Also notice that 4-5 = -1 and this is the coefficient of the middle term. So we try:

Apply the zero product principle:
and/or
If then
If then
The roots are:

(d)
Notice that both sides are perfect squares.
Take the square root of both sides.

or Divide both sides by 3.
or