SOLUTION: How should I completely factor this expression? 144-9p^2 Thanks

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Question 1062328: How should I completely factor this expression?

144-9p^2

Thanks
Found 4 solutions by Alan3354, math_helper, ikleyn, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
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144-9p^2
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You can factor out a 9 first.
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It's a difference of 2 squares.
a%5E2+-+b%5E2+=+%28a-b%29%2A%28a%2Bb%29
Know that.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that 144 is a perfect square (12*12)
and that 9p^2 is also a perfect square ((3p)(3p))...
When you have the form +a%5E2-b%5E2 (i.e. the difference between two squares) you can factor it to +%28a%2Bb%29%28a-b%29+ (I encourage you to multiply (a+b)(a-b) out for yourself to see that you indeed get a%5E2-b%5E2
If I let a=12 and b=3p:
+%2812-3p%29%2812%2B3p%29+=+144-9p%5E2+
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Depending on how far you want to take it, a "3" can be factored out from each of the above factors:
= +3%2A3%2A%284-p%29%284%2Bp%29+ = +9%2A%284-p%29%284%2Bp%29+

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
The shortcut quadratic multiplication formulas are


1. The square of the sum formula is                 %28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2Bb%5E2.
      For details and examples of applications of this formula see the lesson The square of the sum formula


2. The square of the difference formula is     %28a+-+b%29%5E2+=+a%5E2+-+2ab+%2Bb%5E2.
      For details and examples of applications of this formula see the lesson The square of the difference formula


3. The difference of squares formula is       a%5E2+-+b%5E2+=+%28a+%2B+b%29%2A%28a-+b%29.
      For details and examples of applications of this formula see the lesson The difference of squares formula



Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

How should I completely factor this expression?

144-9p^2

Thanks
You MUST FACTOR out a GCF if there is one, and there is indeed one. It's 9.

You then get: 9%2816+-+p%5E2%29. You now factor the DOTS (Difference of 2 squares). You would then have factored the binomial, COMPLETELY.