Question

计算，要有过程

25x²-16y²=
25x²+20xy+4y²=
x³-25x=
3x²+6xy+3y²=
（x-y）²+4xy=
（a+b）²+2（a+b）+1=
（x²+y²）²-4x²y²=
ab+a+b+1=
（x-1）（x-2）-2（2-x）²=
（a²+ab+b²）²-9a²b²=

Answer 1

25x²-16y²
=(5x)²-(4y)²
=(5x+4y)(5x-4y)

25x²+20xy+4y²
=(5x)²+2×5x×2y+(2y)²
=(5x+2y)²

x³-25x
=x(x²-5²)
=x(x+5)(x-5)

3x²+6xy+3y²
=3(x²+2xy+y²)
=3(x+y)²

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

（a+b）²+2（a+b）+1
=[(a+b)+1]²
=(a+b+1)²

（x²+y²）²-4x²y²
=(x²+y²+2xy)(x²+y²-2xy)
=(x+y)²(x-y)²

ab+a+b+1
=a(b+1)+(b+1)
=(b+1)(a+1)

（x-1）（x-2）-2（2-x）²
=(x-1)(x-2)-2(x-2)²
=(x-2)(x-1-2x+4)
=(x-2)(3-x)

（a²+ab+b²）²-9a²b²
=(a²+ab+b²+3ab)(a²+ab+b²-3ab)
=(a²+4ab+b²)(a²-2ab+b²)
=(a²+4ab+b²)(a-b)²