Maths!!! f.3 急

1. 81x2y - 16y(x - y)2
= y[81x2 - 16(x - y)2]
= y[(9x)2 - (4x - 4y)2]
= y(9x - 4x + 4y)(9x + 4x - 4y)
= y(5x + 4y)(13x - 4y)
2. (x + y)4 - (x - y)4
= [(x + y)2]2 - [(x - y)2]2
= [(x + y)2 - (x - y)2][(x + y)2 + (x - y)2]
= [(x + y + x - y)(x + y - x + y)][x2 + 2xy + y2 + x2 - 2xy + y2]
= (2x)(2y)][2x2 + 2y2]
= 8xy(x2 + y2)
3. -2002 + 32x2
= 16(2x2 - 502)
= 16[(√2x)2 - 502]
= 16(√2x - 50)(√2x + 50)
4. 256 - 81x4
= (16)2 - (9x2)2
= (16 - 9x2)(16 + 9x2)
= [42 - (3x)2](16 + 9x2)
= (4 - 3x)(4 + 3x)(16 + 9x2)

1.81x^2y - 16y (x-y) ^2


2.(x+y)^4 - (x-y) ^4
=[(x+y)^2]^2-[(x-y)^2]^2
=[(x+y)^2+(x-y)^2][(x+y)^2-(x-y)^2]
=[(x+y)^2+(x-y)^2](x+y+x-y)(x+y-x+y)
=4xy[(x+y)^2+(x-y)^2]

3. -200^2 + 32x^2


4.256 - 81x^4
=16^2- (9x^2)^2
=(16+9x^2)(16-9x^2)
=(16+9x^2)[4^2-(3x)^2]
=(16+9x^2)(4+3x)(4-3x)