# factoring 16s^4 - 81t^4; solving 144m^2 = 25 and....

#### Princezz3286

##### Junior Member
I have a test monday and I would like to make sure my match is correct can you please verify?

1: Factor Completely: 16s^4 - 81t^4

I broke down into....
(4s^2 - 9t^2)(4s^2 + 9t^2)
I broke that down into.....
(2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t)
is that correct????

Another question I had a question on was

2: Solve 144m^2 = 25

I took the square root of both.....
12m = 5
and divided by 12 to get the variable alone.....
m= 5/12 did i do this correctly?

3: 4q(q - 5) + 14 = 11(2 + q)
4q^2 - 20q + 14 = 22 + 11q
- 11q -22
------------------------------------------
4q^2 - 31q - 8 = 0
(4q + 1) = 0
(q - 8) = 0

q= {-1/4 and 8} right?

#### stapel

##### Super Moderator
Staff member
Princezz3286 said:
1: Factor Completely: 16s^4 - 81t^4....

I broke down into (4s^2 - 9t^2)(4s^2 + 9t^2)
I broke that down into (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t)
What do you mean by having two sets of factors?

Note: You cannot factor a SUM of squares! :shock:

Princezz3286 said:
2: Solve 144m^2 = 25

I took the square root of both: 12m = 5
What happened to the "plus-minus" sign?

Princezz3286 said:
3: 4q(q - 5) + 14 = 11(2 + q)....

q= {-1/4 and 8} right?
To check the answer to any "solving" problem, plug them back into the original problem, and see if they work. In this case, plug "-1/4" in for "q", and see if both sides evaluate to the same number. Then repeat the process, this time plugging "8" in for "q". If they "check", then your answer is correct! :wink:

Eliz.

#### Princezz3286

##### Junior Member
1) The problem was to factor 16s^4 - 81t^4 completely...... so I broke it down by first taking the square root of 16s^4 and 81t^4 and ended up with (4s^2 - 9t^2)(4s^2 + 9t^2), which was I then took the square root of again to get (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t)..... is this wrong? Can you explain why if it is? I am confused!

If I can't factor a sum of squares what is the correct way to do this? I looked in my book to find a similar problem so I could work it backwards, but there was not one......

2) I typed it just as the book had it.....Solve 144m^2 = 25
there was no plus or minus sign..... ????????????

#### Mrspi

##### Senior Member
Princezz3286 said:
1) The problem was to factor 16s^4 - 81t^4 completely...... so I broke it down by first taking the square root of 16s^4 and 81t^4 and ended up with (4s^2 - 9t^2)(4s^2 + 9t^2), which was I then took the square root of again to get (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t)..... is this wrong? Can you explain why if it is? I am confused!

If I can't factor a sum of squares what is the correct way to do this? I looked in my book to find a similar problem so I could work it backwards, but there was not one......

2) I typed it just as the book had it.....Solve 144m^2 = 25
there was no plus or minus sign..... ????????????
If you've got (4s^2 - 9t^2)(4s^2 + 9t^2), you CAN factor the first part into a difference of two squares:

(2s + 3t)(2s - 3t)(4s^2 + 9t^2)

Now...the second part is a SUM of two squares. There is no way to factor that over the real numbers. You may want to talk to your teacher about this.

#### Mrspi

##### Senior Member
Princezz3286 said:
2) I typed it just as the book had it.....Solve 144m^2 = 25
there was no plus or minus sign..... ????????????

If 144m^2 = 25, then

144m^2 - 25 = 0

Factor the left side. Set each factor equal to 0, and solve for m...

If you are still having trouble with this one, please repost, showing all of the work you've done to try to solve it, so we can see how best to help you.

#### Princezz3286

##### Junior Member
ok, I got the 144m^5 = 25 I had done it this way, but I did not have the 2 part answer that I got when I set the equation to 0 and worked the problem.......

Solve 144m^2 = 25
I took the square root of both.....
12m = 5
and divided by 12 to get the variable alone.....
m= 5/12..........

Can you maybe help me do this problem.....
Factor Completely: 16s^4 - 81t^4....

I broke down into (4s^2 - 9t^2)(4s^2 + 9t^2)
I broke that down into (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t) is this correct or wrong?

#### Mrspi

##### Senior Member
Princezz3286 said:
ok, I got the 144m^5 = 25 I had done it this way, but I did not have the 2 part answer that I got when I set the equation to 0 and worked the problem.......

Solve 144m^2 = 25
I took the square root of both.....
12m = 5
and divided by 12 to get the variable alone.....
m= 5/12..........

Can you maybe help me do this problem.....
Factor Completely: 16s^4 - 81t^4....

I broke down into (4s^2 - 9t^2)(4s^2 + 9t^2)
I broke that down into (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t) is this correct or wrong?

If 144m^2 = 25

AND you take the square root of both sides,

You need to remember that there are TWO square roots of 25....+5 and -5. So,

sqrt(144m^2) = +/- sqrt(25)

12m = +/- 5

12 m = 5, OR 12m = -5

Now, proceed from there to find the value(s) of m.

I hope this helps you.

#### Princezz3286

##### Junior Member

Factor Completely: 16s^4 - 81t^4....

I broke down into (4s^2 - 9t^2)(4s^2 + 9t^2)
I broke that down into (2s - 3t)(2s + 3t) and (2s + 3t)(2s + 3t) is this correct or wrong?

#### Denis

##### Senior Member
Princezz3286 said: