Question

2x^3(x^3+1)-x^3(x^3+1)+x^3+1
b) (x^2+x+1)^2-x^2-x-1
c) 16(x+1)^2-9(y+1)^2
d) x^4-1
e) (x^2+2x+3)^2-x^2(x+1)^2

Answer 1

a) 2x^3(x^3+1)-x^3(x^3+1)+x^3+1
= 2x^6 +2x^3 - x^6 -x^3 + x^3 +1
= x^6 + 2x^3 +1
b) (x^2+x+1)^2-x^2-x-1
= x^4 +x^2 +1 -x^2 -x -1
= x^4 -x 
c) 16(x+1)^2 -9(y+1)^2
= 16(x^2 +2x +1) -9(y^2 +2y +1)
= 16x^2 +32x +16 -9y^2 -18y -9
= 16x^2 +32x -9y^2 -18y +7
d) x^4-1
= (x -1)(x^3 +x^2 +x +1)
= (x^2 +1)(x +1)(x -1)
= (x +1)(x -1)(x^2 +1)
e) (x^2+2x+3)^2 -x^2(x+1)^2
= x^4 +4x^2 +9 -x^2(x^2 +2x +1)
= x^4 +4x^2 +9 -x^4 -2x^3 -x^2
= 3x^2 -2x^3 +9
= 2x^3 -3x^2 -9