Question

How do you factor these:
1. 16b^2 - 4c^2
2. 100y^16 - 64x^16

Answer 1

Hey, 1. what can we factor out of the equation?

Answer 2

I'm not sure...

Answer 3

Ok so what is the GCF of this equation or what number can go into both 4 and 16

Answer 4

4

Answer 5

Great, any variables can be factored?

Answer 6

b and c?

Answer 7

No, they arent like terms so just 4 so what is 4 divided by each number

Answer 8

4 and 1

Answer 9

So what do we have left?

Answer 10

4b^2 -c^2

Answer 11

you forgot the 4 so we have\[4(4b ^{2}-c ^{2})\]

Answer 12

Do you think we are done?

Answer 13

no we have to factor out the expression in the parenthesis further

Answer 14

Whats it called? difference of ??

Answer 15

ugh idk sorry

Answer 16

if we have something \(x\) and we take \(x*x = x^2\) what have we done to \(x\)?

Answer 17

Its called difference of perfect squares

Answer 18

ohhhhhhh

Answer 19

so a2-b2=(a+b)(a-b)

Answer 20

ya

Answer 21

So whats 4 squared ?

Answer 22

2

Answer 23

\(4\) squared means \(4*4\)

Answer 24

How about C

Answer 25

would it be (2b^2 - c) (2b^2 - c)

Answer 26

i mean + c

Answer 27

for the second

Answer 28

and then add the 4 outside the parenthesis

Answer 29

Where id you get the 2b^2

Answer 30

You split the ^2 into two parenthesis

Answer 31

bc 2b * 2b is 4b^2

Answer 32

Yes its 2b not 2b^2

Answer 33

oh ya sorry thats what i meant

Answer 34

And + and -

Answer 35

So whats the final answer?

Answer 36

4(2b -c) (2b + c)

Answer 37

Correct :D

Answer 38

Try the next one, tell me what you get

Answer 39

ok

Answer 40

I'm stuck at 4(24y^16 - 16x^16)

Answer 41

16 divdied by 2?

Answer 42

8

Answer 43

wouldnt it be -8

Answer 44

No because 16 is not negative only 16 is

Answer 45

?

Answer 46

64 dvided by = 16 and its -16 but ^16 is positive

Answer 47

but arent u dividing by -64?

Answer 48

Yes so we get -16x^16

Answer 49

so what do we do after this 4(24y^16 - 16x^16)

Answer 50

25

Answer 51

4(25y^16 - 16x^16)

Answer 52

Remember difference of perfect squares ?

Answer 53

ok lemme try

Answer 54

i give up

Answer 55

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

Answer 56

@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 \(x^2*x^2 = x^{2+2} = x^4\)

Answer 57

4(5y^8 - 4x^8) (5y^8+ 4x^8)

Answer 58

yes, that is correct!

You can check that is correct by multiplying it out:
\[4(5y^8-4x^8)(5y^8+4x^8) = 4(25y^{16} + 20x^8y^8-20x^8y^8-16x^{16})\]\[=4(25y^{16}-16x^{16}) = 100y^{16}-64x^{16}\checkmark \]

Answer 59

ok thx so much

Answer 60

Sorry for leaving, had to do some studying, but great job

Answer 61

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