Question on how to factor these problems? Any Help...please.?

Question

5x^2 – 125

x^4 – y^4

x^2 –4x – 45

Answer 1

hi  

1:

=5(x^2-25)=5(x-5)(x+5)

2:

  = (x^2-y^2)(x^2+y^2)= (x-y)(x+y)(x^2+y^2)

3:

= x^2-4x-45 =x^2-4x+4-4 -45=(x^2-4x+4)-49

= (x-2)^2-49 =[x-2-7][x-2+7]=(x-9)(x+5)

Answer 2

5x^2 – 125

5x^2 is divisible by 5x & x

-125  is divisible by 5 and -25 ; -5 & 25

factor is:

(5x - 25) (x+5) ----> ans

: you must take this 5 and -25  so that it comes up with  - 125

x^4 – y^4

x^4 ----> x^2 . x^2

-y^4 ----> y^2 . (-y^2)

(x^2 +  y^2) ( x^2 - y^2) ----> answer



x^2 –4x – 45

x^2  =  x . x

– 45 = (-9) (5)

: 9 should be neg. so that you will get the middle term (-9) + 5 = (-4)

     not the 5 to be neg. because it will become +4

(x + 5) (x - 9) ----> ans

Answer 3

1:

5(x^2 - 25)   {taking common}

5[(x)^2 - (5)^2]

5(x-5) (x + 5)

Do the others yourself!!!