Question

Factor 16x^4 – b^4 + 10b^2 – 25 completely.

A. (4x^2 + b^2)(2x + b)(2x – b) + 5(2b^2 – 5)

B. (4x^2 – b^2 – 5)(4x^2 + b^2 – 5)

C. (2x – b^2 + 5)(2x + b^2 – 5)(4x^2 + b^2 – 5)

D. (4x^2 – b^2 + 5)(4x^2 + b^2 – 5)

Answer 1

Please hepl!

Answer 2

which of the options give u the expression 16x^4 – b^4 + 10b^2 – 25 when distributed

Answer 3

distributive property?

Answer 4

a(b+c)=a*b+a*c-(Distributive property)

Answer 5

i dnt thnk that's a good idea.

Answer 6

Hmm ok. I'm confused :(

Answer 7

@hartnn

Answer 8

really sorry for confusing u

Answer 9

16x^4 – b^4 + 10b^2 – 25
= 16x^4 - (b^4 -10 b^2 +25)

can you first try to factor (b^4 -10 b^2 +25) ??
hint : its a perfect square ?

Answer 10

No no I am sorry for bothering you

Answer 11

Ok I will try

Answer 12

Is it b^6-15

Answer 13

@hartnn

Answer 14

how you got that ?

Answer 15

ok,for factorizing the standard quadratic equation,\( ax^2+bx+c=0\), we need 2 numbers whose sum is 'b' and product = ac
for your Question ,\( (b^4 -10 b^2 +25) = ( (b^2)^2 -10 (b^2) +25)\)
can you find 2 numbers whose sum = -10 and product = 25 ?

Answer 16

-5 and -5

Answer 17

yes, so can you factorize that now by writing -10b^2 = -5b^2-5b^2
??

Answer 18

Yes

Answer 19

what u get after factoring ?

Answer 20

I don't know:(

Answer 21

(b^4−5b^2-5b^2+25)
now factor out b^2 from first 2 terms and -5 from last 2 terms, what u get ?

Answer 22

(b^2-5)^2

Answer 23

yes, thats correct :)
so now you have
\(16x^4-(b^2-5)^2 = (4x^2)-(b^2-5)^2\)
use the difference of squares formula \(a^2-b^2=(a+b)(a-b)\) to factor that

Answer 24

16x^4 + b^4 - 50

Answer 25

I think it's not correct :(

Answer 26

use 4x^2 as 'a' and (b^2-5) as 'b'

Answer 27

so 4x^2-(b^2-5)

Answer 28

that is just a-b
what about a+b ?

Answer 29

4x^2-(b^2-5) = 4x^2+(b^2+5)

Answer 30

Is it correct?

Answer 31

what that = in between ?
its
(4x^2-(b^2-5))( 4x^2+(b^2-5))
= .....?

Answer 32

oh sorry :(

Answer 33

so it is (4x^2-(b^2-5))( 4x^2+(b^2-5))

Answer 34

thats what i typed, one step of simplification and you'll get your answer.

Answer 35

(4x^2 – b^2 – 5)(4x^2 + b^2 – 5)

Answer 36

Is it correct?

Answer 37

yes

Answer 38

Thank you very much :)

Answer 39

welcome ^_^