AmberlyKhan
  • AmberlyKhan
How do you factor these: 1. 16b^2 - 4c^2 2. 100y^16 - 64x^16
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jagr2713
  • jagr2713
Hey, 1. what can we factor out of the equation?
AmberlyKhan
  • AmberlyKhan
I'm not sure...
jagr2713
  • jagr2713
Ok so what is the GCF of this equation or what number can go into both 4 and 16

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More answers

AmberlyKhan
  • AmberlyKhan
4
jagr2713
  • jagr2713
Great, any variables can be factored?
AmberlyKhan
  • AmberlyKhan
b and c?
jagr2713
  • jagr2713
No, they arent like terms so just 4 so what is 4 divided by each number
AmberlyKhan
  • AmberlyKhan
4 and 1
jagr2713
  • jagr2713
So what do we have left?
AmberlyKhan
  • AmberlyKhan
4b^2 -c^2
jagr2713
  • jagr2713
you forgot the 4 so we have\[4(4b ^{2}-c ^{2})\]
jagr2713
  • jagr2713
Do you think we are done?
AmberlyKhan
  • AmberlyKhan
no we have to factor out the expression in the parenthesis further
jagr2713
  • jagr2713
Whats it called? difference of ??
AmberlyKhan
  • AmberlyKhan
ugh idk sorry
whpalmer4
  • whpalmer4
if we have something \(x\) and we take \(x*x = x^2\) what have we done to \(x\)?
jagr2713
  • jagr2713
Its called difference of perfect squares
AmberlyKhan
  • AmberlyKhan
ohhhhhhh
jagr2713
  • jagr2713
so a2-b2=(a+b)(a-b)
AmberlyKhan
  • AmberlyKhan
ya
jagr2713
  • jagr2713
So whats 4 squared ?
AmberlyKhan
  • AmberlyKhan
2
whpalmer4
  • whpalmer4
\(4\) squared means \(4*4\)
jagr2713
  • jagr2713
How about C
AmberlyKhan
  • AmberlyKhan
would it be (2b^2 - c) (2b^2 - c)
AmberlyKhan
  • AmberlyKhan
i mean + c
AmberlyKhan
  • AmberlyKhan
for the second
AmberlyKhan
  • AmberlyKhan
and then add the 4 outside the parenthesis
jagr2713
  • jagr2713
Where id you get the 2b^2
jagr2713
  • jagr2713
You split the ^2 into two parenthesis
AmberlyKhan
  • AmberlyKhan
bc 2b * 2b is 4b^2
jagr2713
  • jagr2713
Yes its 2b not 2b^2
AmberlyKhan
  • AmberlyKhan
oh ya sorry thats what i meant
jagr2713
  • jagr2713
And + and -
jagr2713
  • jagr2713
So whats the final answer?
AmberlyKhan
  • AmberlyKhan
4(2b -c) (2b + c)
jagr2713
  • jagr2713
Correct :D
jagr2713
  • jagr2713
Try the next one, tell me what you get
AmberlyKhan
  • AmberlyKhan
ok
AmberlyKhan
  • AmberlyKhan
I'm stuck at 4(24y^16 - 16x^16)
jagr2713
  • jagr2713
16 divdied by 2?
AmberlyKhan
  • AmberlyKhan
8
AmberlyKhan
  • AmberlyKhan
wouldnt it be -8
jagr2713
  • jagr2713
No because 16 is not negative only 16 is
AmberlyKhan
  • AmberlyKhan
?
jagr2713
  • jagr2713
64 dvided by = 16 and its -16 but ^16 is positive
AmberlyKhan
  • AmberlyKhan
but arent u dividing by -64?
jagr2713
  • jagr2713
Yes so we get -16x^16
AmberlyKhan
  • AmberlyKhan
so what do we do after this 4(24y^16 - 16x^16)
AmberlyKhan
  • AmberlyKhan
25
AmberlyKhan
  • AmberlyKhan
4(25y^16 - 16x^16)
jagr2713
  • jagr2713
Remember difference of perfect squares ?
AmberlyKhan
  • AmberlyKhan
ok lemme try
AmberlyKhan
  • AmberlyKhan
i give up
jagr2713
  • jagr2713
Sorry i have finals tomorrow and i cant stay but just divided the exponents by 2 and you will get your answer and dont forget to sqrt 25 and 16
whpalmer4
  • whpalmer4
@AmberlyKhan \[4(25y^{16} - 16x^{16})\]Let's just look at \(25y^{16}\)and see if we can recognize it as something that is a perfect square. what number times itself = 25? what power of \(y\) times itself = \(y^{16}\)? remember that when you multiply exponentials with the same base, you keep the base and add the exponents, so \(x^2*x^2 = x^{2+2} = x^4\)
AmberlyKhan
  • AmberlyKhan
4(5y^8 - 4x^8) (5y^8+ 4x^8)
whpalmer4
  • whpalmer4
yes, that is correct! You can check that is correct by multiplying it out: \[4(5y^8-4x^8)(5y^8+4x^8) = 4(25y^{16} + 20x^8y^8-20x^8y^8-16x^{16})\]\[=4(25y^{16}-16x^{16}) = 100y^{16}-64x^{16}\checkmark \]
AmberlyKhan
  • AmberlyKhan
ok thx so much
jagr2713
  • jagr2713
Sorry for leaving, had to do some studying, but great job
jagr2713
  • jagr2713
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