HELP..!! Factoring?

Question

a) Factor one expression by grouping terms

x^5+x^4+x+1

b) Factor one expression completely

(a^2-1) b^2-4 (a^2-1)

c) Factor one expression completely. Begin by factoring out the lowest power of each common factor

x^-1/2 (x+1)^1/2 + x^1/2 (x+1)^-1/2

Answer 1

a) x^5 + x^4 + x + 1
= x^4(x+1) + 1(x+1) = (x+1)(x^4 +1)

b) (a^2 -1)b^2 - 4(a^2 -1) = (a^2 -1)(b^2 -4)
= (a-1)(a+1)(b-2)(b+2)

c) x^-1/2 (x+1)^1/2 + x^1/2 (x+1)^-1/2
= x^-1/2 (x+1)^-1/2 [(x+1) + x]
= x^-1/2 (x+1)^-1/2 (2x+1)

Answer 2

a) x(x^4 + 1) + (x^4 + 1) = (x^4 + 1)(x + 1)

b) (a^2 - 1)(b^2 - 4) = (a + 1)(a - 1)(b + 2)(b - 2)