[tex]1-256v^8 = 1 -(16v^4)^2 = (1 + 16v^4)(1-16v^4) = [/tex] [tex](1+16v^4) (1 - (4v^2)^2)= (1 + 16v^4)(1 + 4v^2)(1-4v^2) [/tex]
= [tex](1 + 16v^4)(1 + 4v^2) (1- (2v)^2) =(1 + 16v^4)(1 + 4v^2) (1+2v)(1-2v)[/tex]
2) [tex]x^6 +7x -8 = (x-1) (x^5 +x^4 +x^3 +x^2 +x + 8 )[/tex]
3) [tex]x^2 -3 = x^2 - (\sqrt{3})^2 = (x +\sqrt{3}) (x -\sqrt{3}) = -(\sqrt{3} + x) (\sqrt{3}-x)[/tex]
4) [tex]5y^2 - 1 = (\sqrt{5}y)^2 - (1)^2= (\sqrt{5}y +1)(\sqrt{5}y-1)[/tex]
5) [tex]a^2 -2b^2 = a^2 -(\sqrt{2}b)^2 = (a +\sqrt{2}) ( a -\sqrt{2})[/tex]
