急...(10點)關於Factorize既數

1) 3x^2-75
3(x^2-25)
3(x^2-5^2)
3(x +5)(x – 5)

2) 5y^2-30y+45
5(y^2-6y+9)
5(y + 3)(y+3)

3) x^2+2x+y+xy+1
x^2+ 2x +1+ xy + y
(x + 1)(x + 1) + y(x + 1)
(x + 1) (x + 1 +y)

4)m^2+m^2n+2mn+mn^2+n^2
m^2+2mn+n^2 + mn^2+m^2n
(m + n)(m + n) +mn(n + m)
(m + n)(m + n + mn)

5) m^2 - 4mn +4n^2 -(m+n)^2
m^2 - 4mn +4n^2 - m^2 -2mn - n^2
6mn + 3n^2
3n^2 – 6mn
3n(n – 2m)

6) (2x+1)^2-x^4
(2x + 1 +x^2)(2x + 1 –x^2)
(x+1)^2 (2x + 1 –x^2)

7) Prove the identity x^3+y^3≡(x+y)(x^2-xy+y^2)
(x+y)(x^2-xy+y^2) = x^3 –(x^2)y +x(y^2) + y(x^2) – x(y^2) + y^3
(x+y)(x^2-xy+y^2) = x^3 + y^3

Prove the identity x^3-y^3≡(x-y)(x^2+xy+y^2)
(x-y)(x^2-xy+y^2) = x^3 –(x^2)y +x(y^2) - y(x^2) + x(y^2) - y^3
(x-y)(x^2-xy+y^2) = x^3 - y^3

Hence factorize x^6-y^6
(x^2)^3 – (y^2)^3
(x^2- y^2)(x^4+(xy)^2+ y^4)
(x + y)(x- y)(x^4+(xy)^2 + y^4)