Question

Упростите выражения: 1) 3a(a+2)-(a+3)² 2) 3(y-1)²+6y 3) 8c+4(1-c)² 4) 4ab+2(a-b)² 5) 3(x+y)²-6xy

Answer 1

1) 3a(a+2)-(a+3)²= 3a(a+2)-(a+3)(a+3)=3a²+6a-(a²+6a+9)=2a²-9

2) 3(y-1)²+6y = 3(y-1)(y-1)+6y=3(y²-2y+1)+6y=3y²-6y+3+6y=3y²+3=3(y²+1)

3) 8c+4(1-c)² = 8c+4(1-2c+c²)=8c+4-8c+4c²=4(c²+1)

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

5) 3(x+y)²-6xy = 3(x²+2xy+y²)-6xy=3x²+6xy+3y²-6xy=3(x²+y²)