Factor completley 5a^2 - 125
show the work because I want to learn how to do this the right way
2006-10-08 15:18:10 · 7 answers · asked by jazminda S 1 in Science & Mathematics ➔ Mathematics
1. 5a^2 - 125) original equation
2. 5(a^2 - 25) take out a 5
3. 5(a + 5)(a - 5) factor a^2 -25
I hop this helped
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2006-10-08 15:36:18 · answer #1 · answered by wormhole 2 · 0⤊ 0⤋
To factor 5a^2 - 125, find a BIG number that can evenly be divided into 5 and 125.
I would say 5 is a very good choice.
So, remove 5 and set it outside parentheses.
How many times does 5 go into 5? The answer is 1.
Then, ask yourself: how many times does 5 go into 125?
The answer is 25.
We write the answer in factored form this way:
5(a^2 - 25).
However, we can factor what is inside the parentheses.
What is inside the parentheses is called THE DIFFERENCE OF TWO PERFECT SQUARES.
What two numbers, that are the same number, when multiplied together will produce -25? How about +5 times -5? Yes, this will work.
Final answer: 5(a - 5) (a + 5)
I hope this helps.
Guido
P.S. Note that 5, (a - 5) and (a + 5) are ALL factors of the original question.
2006-10-08 15:28:21 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Any time you have an equation which is the difference of two perfect squares n^2-m^2 the factors are (n+m)(n-m).
Multiply these out to convince yourself.
Your equation is 5a^2-125.
Divide by 5 you get 5(a^2-25)
a^2 and 25 are both perfect squares so the factors are
(a+5)(a-5)5.
Those are the three factors.
2006-10-08 15:40:06 · answer #3 · answered by True Blue 6 · 0⤊ 0⤋
5(x - 5)(x + 5) Here's how: You have 5x2 -125. Stick a 0x in the middle. 5x2 +0x -125 You now have a trinomial. Think: What factors of -625 (you multiply 5 by -125) add up to zero? 25 and -25. Rewrite the equation: 5x2 +25x -25x -125. Pull out the greatest common factor from the 5x2 and the 25x. This is 5x. Next, pull out the greatest common factor from -25x and -125. This is -25. Rewrite: 5x(x+5) -25(x+5) Notice you have (x+5) twice. Write (x+5) as the first part of your equation. The second comes from the two outside numbers, 5x and -25. It will be written as (5x-25). You now have: (5x-25)(x+5) You can still factor. The greatest common factor of 5 and -25 is five. Pull that out. Your answer: 5(x-5)(x+5)
2016-03-28 02:10:49 · answer #4 · answered by ? 4 · 0⤊ 0⤋
5a^2 - 125 1st factor out 5
5(a^2-25) this binomial has the form a^2-b^2=(a+b)(a-b)
5(a+5)(a-5)
2006-10-11 13:02:18 · answer #5 · answered by yupchagee 7 · 0⤊ 0⤋
5a^2 - 125 = 5(5a^2 - 25) = 5(a-5)(a+5)
2006-10-08 15:29:47 · answer #6 · answered by qwert 5 · 0⤊ 0⤋
5a^2-125
5(a^2-25)
5(a+5)(a-5)
2006-10-08 15:19:32 · answer #7 · answered by Greg G 5 · 0⤊ 0⤋