有關factorization的題目

1) x③－xy②
= x ( x② - y②)
= x ( x - y ) ( x + y )

2) 4+12n+9n②
= 2② + 2(2)(3)n +(3n)②
= (2+3n)②

3) 16u②－72uv+81v②
= (4u)②－(2)(4u)(9v)+(9v)②
= (4u - 9v)②

4) 16(p-5)②+8(p-5)+1
= [4(p-5)]②+2[4(p-5)]+1
= [4(p-5)+1]
= (4p - 19)

5) 4(x-y)②－4z(x-y)+z②
= [2(x-y)]② - 2(z)[2(x-y)] +z②
= [2(x-y) - z]②
= (2x-2y-z)②

6) w④+18w②x②+81x④
= (w②)② + 2(w②)(9x)② + (9x②)②
= (w②+9x②)②

7) m④－18m②+81
= (m②)② - 2(m②)(9②) + 9②
= (m②-9)②

8) 16p④－8p②q②+q④
= (4p②)② - 2(2p②)(q②) + (q②)②
= (4p② - q②)②
= (2p - q)②(2p + q)②

9a)1-6t②+9t④
= 1 - 2(3t②) + (3t②)②
= (1-3t②)②

9b)1-6t②+9t④-121s②
= ( 1 - 6t② +9t④ ) - 121s②
= (1-3t②)② - (11s)②
= ( 1 - 3t②- 11s) (1-3t②+11s)

1) x(x^2 - y^2)
=x(x+y)(x-y)
2) (2+3n)^2
3) (4u+9v)(4u-9v)
4) (4(p-5)+1)^2
=(4p-19)^2
5) (2(x-y)-z)^2
=(2x-2y-z)^2
6) (w^2+9x^2)^2
7) (m-9)^2
8) (4p^2-q^2)^2
=((2p+q)(2p-q))^2
=(2p+q)^2(2p-q)^2
9a) (1-3t^2)^2
=((1+sqrt(3)t)(1-sqrt(3)t))^2
=(1+sqrt(3)t)^2(1-sqrt(3)t)^2
9b) (1-3t)^2 - 121s^2
=(1-3t+11s)(1-3t-11s)

Note: ^2 = ②