Bài 1:
`a)(1+3y)²`
`=1²+2.1.3y+(3y)²`
`=1²+6y+9y²`
`(5x+y)²`
`=(5x)²+2.5x.y+y²`
`=25x²+10xy+y²`
`(x+0,25)²`
`=x²+2.x.0,25+0,25²`
`=x²+0,5x+0,0625`
`b)(x-1/2)^2`
`=x²-2.x. 1/2+(1/2)^2`
`=x²-x+1/4`
`(1/3x-1/2y)^2`
`=(1/3x)^2 -2. 1/3x . 1/2y+(1/2y)^2`
`=1/9x²-1/3xy+1/4y²`
`c)(5x+y)(5x-y)`
`=(5x)²-y²`
`=25x²-y²`
`(x²-2/5y)(x²+2/5y)`
`=(x²)^2-(2/5y)^2`
`=x^4-4/25y²`
`(a²+3)(3-a²)`
`=(3+a²)(3-a²)`
`=3²-(a²)^2`
`=9-a^4`
Bài 2:
`a)x^2-6x+9`
`=x^2-2.x.3+3^2`
`=(x-3)^2`
`b)x^2+x+1/4`
`=x^2+2.x. 1/2+(1/2)^2`
`=(x+1/2)^2`
`c)4x^2-1/16`
`=(2x)^2-(1/4)^2`
`=(2x+1/4)(2x-1/4)`
`d)(a+b)^2-4`
`=(a+b)^2-2^2`
`=(a+b+2)(a+b-2)`
`e)(a²+9)^2-36a²`
`=(a²+9)^2-(6a)^2`
`=(a²+9+6a)(a²+9-6a)`
`=(a²+2.a.3+3²)(a²-2.a.3+3²)`
`=(a+3)²(a-3)²`
`f)(2x+3y)²+2.(2x+3y).y+y²`
`=(2x+3y+y)²`
`=(2x+4y)²`
`g)x²+2x.(y+1)+y²+2y+1`
`=x²+2.x.(y+1)+(y²+2y+1)`
`=x²+2.x.(y+1)+(y+1)²`
`=(x+y+1)²`
Bài 3:
`a)(x+8)(x+6)-x²=104`
`⇔x²+6x+8x+48-x²=104`
`⇔(x²-x²)+(6x+8x)+48=104`
`⇔14x+48=104`
`⇔14x=104-48`
`⇔14x=56`
`⇔x=56:14`
`⇔x=4`
Vậy `x=4`
`b)6x²-(2x-3)(3x+2)-1=0`
`⇔6x²-(6x²+4x-9x-6)-1=0`
`⇔6x²-6x²-4x+9x+6-1=0`
`⇔(6x²-6x²)+(-4x+9x)+(6-1)=0`
`⇔5x+5=0`
`⇔5x=-5`
`⇔x=(-5):5`
`⇔x=-1`
Vậy `x=-1`
`c)(x+4)²-(x+1)(x-1)=16`
`⇔x²+8x+16-(x²-1)=16`
`⇔x²+8x+16-x²+1=16`
`⇔(x²-x²)+8x+(16+1)=16`
`⇔8x+17=16`
`⇔8x=16-17`
`⇔8x=-1`
`⇔x=-1/8`
Vậy `x=-1/8`
`d)(10x+9)x-(5x-1)(2x+3)=8`
`⇔10x²+9x-(10x²+15x-2x-3)=8`
`⇔10x²+9x-10x²-15x+2x+3=8`
`⇔(10x²-10x²)+(9x-15x+2x)+3=8`
`⇔-4x+3=8`
`⇔-4x=8-3`
`⇔-4x=5`
`⇔x=-5/4`
Vậy `x=-5/4`
`e)(2x-1)²+(x+3)²-5(x+7)(x-7)=0`
`⇔4x²-4x+1+x²+6x+9-5(x²-49)=0`
`⇔4x²-4x+1+x²+6x+9-5x²+245=0`
`⇔(4x²+x²-5x²)+(-4x+6x)+(1+9+245)=0`
`⇔2x+255=0`
`⇔2x=-255`
`⇔x=-255/2`
Vậy `x=-255/2`
`f)x(x+1)(x+6)-x³=5x`
`⇔(x²+x)(x+6)-x³=5x`
`⇔x³+6x²+x²+6x-x³-5x=0`
`⇔(x³-x³)+(6x²+x²)+(6x-5x)=0`
`⇔7x²+x=0`
`⇔x(7x+1)=0`
`⇔`\(\left[ \begin{array}{l}x=0\\7x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=0\\x=\dfrac{-1}{7}\end{array} \right.\)
Vậy `x=0` hoặc `x=-1/7`
