Bài 1:
`a)(2x-3)²-(2x+1)(x-1)`
`=(2x)²-2.2x.3+3²-(2x²-2x+x-1)`
`=4x²-12x+9-2x²+2x-x+1`
`=(4x²-2x²)+(-12x+2x-x)+(9+1)`
`=2x²-11x+10`
`b)(3x+1)²-x(2-x)`
`=(3x)²+2.3x.1+1²-2x+x²`
`=9x²+6x+1-2x+x²`
`=(9x²+x²)+(6x-2x)+1`
`=10x²+4x+1`
Bài 2:
`a)(x-2)²-x(x+2)=5`
`⇔x²-2.x.2+2²-x²-2x=5`
`⇔x²-4x+4-x²-2x=5`
`⇔(x²-x²)-(4x+2x)+4=5`
`⇔-6x+4=5`
`⇔-6x=5-4`
`⇔-6x=1`
`⇔x=-1/6`
Vậy `x=-1/6`
`b)(2x-1)²=16`
`⇔(2x-1)²-16=0`
`⇔(2x-1)²-4²=0`
`⇔(2x-1+4)(2x-1-4)=0`
`⇔(2x+3)(2x-5)=0`
`(1)2x+3=0⇔2x=-3⇔x=-3/2`
`(2)2x-5=0⇔2x=5⇔x=5/2`
Vậy `x∈{-3/2;5/2}`
`c)(2x+1)²-3x(x+1)-x²=10`
`⇔(2x)²+2.2x.1+1²-3x²-3x-x²=10`
`⇔4x²+4x+1-3x²-3x-x²=10`
`⇔(4x²-3x²-x²)+(4x-3x)+1=10`
`⇔x+1=10`
`⇔x=10-1`
`⇔x=9`
Vậy `x=9`
Bài 3:
`a)95.105`
`=(100-5)(100+5)`
`=100²-5²`
`=10` `000-25`
`=9` `975`
`b)35²+70.65+65²`
`=35²+2.35.65+65²`
`=(35+65)²`
`=100²`
`=10` `000`
Bài 4:
`a)4x²-4x+1`
`=(2x)²-2.2x.1+1²`
`=(2x-1)²`
`b)x²-4xy+4y²`
`=x²-2.x.2y+(2y)²`
`=(x-2y)²`