幾條因式分解唔識做...

1.
令 u = a² + 2a

(a² + 2a)² - 2(a² + 2a) - 3
= u² - 2u - 3
= (u - 3)(u + 1)
= (a² + 2a - 3)(a² + 2a + 1)
= (a² + 2a - 3) [a² + 2a(1) + (1)²]
= (a + 3)(a - 1)(a + 1)²


2.
令 u = x + 1

x²y + 2xy +y - y³
= y[x² + 2x + 1 - y²]
= y[(x² + 2x + 1) - y²]
= y[(x² + 2*x*1 + 1²) - y²]
= y[(x + 1)² - y²]
= y(u² - y²)
= y(u + y)(u - y)
= y[(x + 1) + y] [(x + 1) - y]
= y(x + y + 1)(x - y + 1)


3.
令 u = y + 1

x² - y² - 2y - 1
= x² - (y² + 2y + 1)
= x² - [y² + 2y(1) + (1)²]
= x² - (y + 1)²
= x² - u²
= (x + u)(x - u)
= [x + (y + 1)] [x - (y + 1)]
= (x + y + 1)(x - y - 1)


4.
令 u = a + 2b

a² + 4ab + 4b² - 2a - 4b + 1
= (a² + 4ab + 4b²) - (2a + 4b) + 1
= [a² + 2a(2b) + (2b)²] - 2(a + 2b) + 1
= (a + 2b)² - 2(a + b) + 1
= u² - 2u + 1
= u² - 2u(1) + (1)²
= (u - 1)²
= (a + 2b - 1)²

1.(a^2+2a)^2-2(a^2+2a)-3
設x=(a^2+2a)
=x^2-2x-3
=(x-3)(x+1)
=[(a^2+2a)-3][(a^2+2a)+1]
=(a^2+2a-3)(a^2+2a+1)
=(a+3)(a-1)(a+1)^2

2.x^2y+2xy+y-y^3
=y(x^2+2a+1-y^2)
=y[(x+1)^2-y^2]
=y(x-y+1)(x+y+1)

3.X^2-y^2-2y-1
=x^2-(y^2+2y+1)
=[x-(y+1)][x+(y+1]
=(x-y-1)(x+y+1)

4.a^2+4ab+4b^2-2a-4b+1
設x=a+2b
a^2+4ab+4b^2-2a-4b+1
=(a+2b)^2-2(a+2b)+1
=x^2-2x+1
=(x-1)^2
=(a+2v-1)^2