Question

2006^2. (2a+b)(2a-b)+3(2a-b)^2. (2x-3y)^2-(y+3x)(3x-y) [(x-y)^2+(x+y)^2](x^2-y^2)

要过程

Answer 1

2006^2.
=(2000+6)²
=2000²+2×2000×6+6²
=4000000+12 000+36
=4012036

(2a+b)(2a-b)+3(2a-b)^2.
=(2a-b)(2a+b+6a-3b)
=(2a-b)(8a-2b)
=16a²-4ab-8ab+2b²
=16a²-12ab+2b²

(2x-3y)^2-(y+3x)(3x-y)
=(4x²-12xy+9y²)-(9x²-y²)
=4x²-12xy+9y²-9x²+y²
=-5x²-12xy+10y²

[(x-y)^2+(x+y)^2](x^2-y^2)
=(x²-2xy+y²+x²+2xy+y²)(x²-y²)
=2(x²+y²)(x²-y²)
=2(x^4-y^4)
=2x^4-2y^4