1.а)
(a+b)²=a²+2ab+b² a²+b²≠a²+2ab+b²
Ответ: нет.
1.б)
(a-b)²+4ab=a²-2ab+b²+4a=a²+2ab+b²=(a+b)²
Ответ: да.
2.
(a+2b)²-(a-2b)²=(a+2b+a-2b)(a+2b-a+2b)=2a*4b=8ab.
4.
(x+5)(y+5)-(x-3)(y-3)=xy+5y+5x+25-xy+3y+3x-9=
=8x+8y+16=8*(x+y)+16=8*5+16=40+16=56.
5.
(3x³-12x)/(x*(x-2)(x+2))=3x*(x²-4)/(x*(x²-4))=3≡6x²/2x².
6.(x⁴-y⁴)/(x+y)-(x-y)³=(x²-y²)(x²+y²)/(x+y)-(x-y)³=
=(x-y)(x+y)(x²+y²)/(x+y)-(x-y)³=(x-y)(x²+y²)-(x-y)³=(x-y)(x²+y²-(x-y)²)=
=(x-y)(x²+y²-x²+2xy-y²)=2xy*(x-y).