How do you factor #768x^4-3y^4#?

1 Answer

Answer:

#3(4x-y)(4x+y)(16x^2 + y^2)#

Explanation:

Algebraic identity:

#(a+b)(a-b) = a^2-b^2#

Factorise out the common factors in # 768x^4-3y^4 #.

#768x^4-3y^4 = 3(256x^4-y^4)#

You can write

#256x^4 - y^4 = (16x^2)^2 - (y^2)^2 = (16x^2 - y^2)(16x^2 + y^2)#

You can write

#16x^2 - y^2 = (4x)^2 - y^2 = (4x-y)(4x+y)#

Put this back together to get

#768x^4 - 3y^4 = 3(4x-y)(4x+y)(16x^2 + y^2)#