Difference of Squares ?

Question

1.Factor 4x^4 - y^2

2.Factor 9x^2 - 8y^2

3.Factor 16x^4 - 4y^2

4.Factor 4x^2 - 64y^2

5.Factor x^2 - 16y^2

Answer 1

a^ 2 - b^ 2 = (a+b)(a-b). 4x^ 4 = (2x^2)^ 2

so 4x^4 - Y^2 = (2x^2 +y)(2x^2-y).

for the rest, remember that  8 = 2^3 = [2 sqrt(2)]^2

64 = 8^2

16 = 4^2

and apply the first formula.  

Answer 2

1. (2x^2+y)(2x^2-y)

2. (3x+2sq.rt.2)(3x-2sq.rt.2)

3. (4x^2+2y)(4x^2-2y)

4. (2x+8y)(2x-8y)

5. (x+4y)(x-4y)

Answer 3

a^2 - b^2 will factor into (a+b)(a-b)

Example:

25p^2 - 4m^2

The 'a^2' in this case is 25p^2, so a is 5p (ask yourself, what number times itself equals the first term?)  Likewise, the 'b^2' is 4m^2, so b is 2m.  Plugging these into the formula,

25p^2 - 4m^2 = (5p + 2m)(5p - 2m)

Go for it.  You can do it!

Answer 4

1. 4x^4 - y^2 = (2x^2)^2 - y^2

                   = (2x^2 - y)(2x^2 + y) (since a^2 - b^2 = (a+b)(a-b))

2. 9x^2 - 8y^2 = (3x)^2-(2sqrt(2)y)^2

                     = (3x-2sqrt(2)y) (3x + 2sqrt(2)y)

use the above mentioned formula to factorise the rest of the problems!!

Answer 5

they are in the format a^2 - b^2 = a+b)( a-b)

1. (2x^2)^2 - (y)^2 = (2x^2+y)( 2x^2- y)

2.  (3x+2sqrt2 y) ( 3x-2sqrt2 y)  note  8  can be made  sq as 2 sqrt2

3. you can do it 4x^2+ 2y and other part

rest all are simple