1.
а) (y-4)²=y²-2y×4+4²=y²-8y+4²=y²-8y+16
б) (7x+a)²=(7x)²+2×7×a+a²=49x²+2×7×a+a²=49x²+14ax+a²
в) (5с-1)(5с+1)=(5с)²-1²=25с²-1
г) (3a+2b)(3a-2b)=(3a)²-(2b)²=9a²-4b²
2.
(c+b)(c-b)-(5c²-b²)=c²-b²-5c²+b²=c²-5c²=-4c²
3.
а) x²-49=x²-7²=(x-7)(x+7)
б) 25x²-10xy+y²=5²x²-2×5x×y+y²=(5x)²-2×5x×y+y²=(5x-y)²
в) x³-9x=x×(x²-9)=x(x-3)(x+3)
г) x²-x-y²-y=(x-y)×(x+y)-(x+y)=(x+y)(x-y-1)
4.
36-(6-x)²=x(2,5-x)
36-(36-12x+x²)=2,5x-x²
36-36+12x-x²=2,5x-x²
12x-x²=2,5x-x²
12x=2,5x
12x-2,5x=0
9,5x=0
x=0
1.
а) (y-4)²=y²-2y×4+4²=y²-8y+4²=y²-8y+16
б) (7x+a)²=(7x)²+2×7×a+a²=49x²+2×7×a+a²=49x²+14ax+a²
в) (5с-1)(5с+1)=(5с)²-1²=25с²-1
г) (3a+2b)(3a-2b)=(3a)²-(2b)²=9a²-4b²
2.
(c+b)(c-b)-(5c²-b²)=c²-b²-5c²+b²=c²-5c²=-4c²
3.
а) x²-49=x²-7²=(x-7)(x+7)
б) 25x²-10xy+y²=5²x²-2×5x×y+y²=(5x)²-2×5x×y+y²=(5x-y)²
в) x³-9x=x×(x²-9)=x(x-3)(x+3)
г) x²-x-y²-y=(x-y)×(x+y)-(x+y)=(x+y)(x-y-1)
4.
36-(6-x)²=x(2,5-x)
36-(36-12x+x²)=2,5x-x²
36-36+12x-x²=2,5x-x²
12x-x²=2,5x-x²
12x=2,5x
12x-2,5x=0
9,5x=0
x=0