Bài 1:
`a)5x²-5xy-7x+7y`
`=5x(x-y)-7(x-y)`
`=(x-y)(5x-7)`
`b)ab-ac-b²+bc`
`=a(b-c)-b(b-c)`
`=(b-c)(a-b)`
`c)3x³-12x=3x(x²-4)=3x(x+2)(x-2)`
`d)x²-4+(x+2)²`
`=(x+2)(x-2)+(x+2)²`
`=(x+2)(x-2+x+2)`
`=2x(x+2)`
`e)x²-25+y²-2xy`
`=(x²-2xy+y²)-25`
`=(x-y)²-5²`
`=(x-y+5)(x-y-5)`
`f)36x²-a²+10a-25`
`=36x²-(a²-10a+25)`
`=(6x)²-(a-5)²`
`=(6x+a-5)(6x-a+5)`
Bài 2:
`a)x²+x-2`
`=x²+2x-x-2`
`=x(x+2)-(x+2)`
`=(x+2)(x-1)`
`b)3x²+7x-6`
`=3x²+9x-2x-6`
`=3x(x+3)-2(x+3)`
`=(x+3)(3x-2)`
`c)8x²-23x-3`
`=8x²-24x+x-3`
`=8x(x-3)+(x-3)`
`=(x-3)(8x+1)`
`d)-10x²-17x+6`
`=-10x²-20x+3x+6`
`=-10x(x+2)+3(x+2)`
`=(x+2)(-10x+3)`
Bài 3:
`a)x³-x²-25x+25=0`
`⇔x²(x-1)-25(x-1)=0`
`⇔(x-1)(x²-25)=0`
`⇔(x-1)(x+5)(x-5)=0`
`⇔`\(\left[ \begin{array}{l}x-1=0\\x+5=0\\x-5=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1\\x=-5\\x=5\end{array} \right.\)
Vậy `x=1` hoặc `x=-5` hoặc `x=5`
`b)4x³-8x²-9x+18=0`
`⇔4x²(x-2)-9(x-2)=0`
`⇔(x-2)(4x²-9)=0`
`⇔(x-2)(2x+3)(2x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-2=0\\2x+3=0\\2x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x-2=0\\x=-\dfrac{3}{2}\\x=\dfrac{3}{2}\end{array} \right.\)
Vậy `x=0` hoặc `x=-3/2` hoặc `x=3/2`
Bài 4:
`a)3x(x-1)+x-1=0`
`⇔3x(x-1)+(x-1)=0`
`⇔(x-1)(3x+1)=0`
`⇔`\(\left[ \begin{array}{l}x-1=0\\3x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1\\x=-\dfrac{1}{3}\end{array} \right.\)
vậy `x=1` hoặc `x=-1/3`
`b)(x-2)(x²+2x+7)+2(x²-4)-5(x-2)=0`
`⇔(x-2)(x²+2x+7)+2(x+2)(x-2)-5(x-2)=0`
`⇔(x-2)[x²+2x+7+2(x+2)-5]=0`
`⇔(x-2)(x²+2x+7+2x+4-5)=0`
`⇔(x-2)(x²+4x+6)=0`
`⇔`\(\left[ \begin{array}{l}x-2=0\\x²+4x+6=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=2\\x²+4x+6=0( vô nghiệm)\end{array} \right.\)
Vậy `x=2`
`c)(2x-1)²-25=0`
`⇔(2x-1)²-5²=0`
`⇔(2x-1+5)(2x-1-5)=0`
`⇔(2x+4)(2x-6)=0`
`⇔`\(\left[ \begin{array}{l}2x+4=0\\2x-6=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}2x=-4\\2x=6\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-2\\x=3\end{array} \right.\)
Vậy `x=-2` hoặc `x=3`
`d)x³+27+(x+3)(x-9)=0`
`⇔(x+3)(x²-3x+9)+(x+3)(x-9)=0`
`⇔(x+3)(x²-3x+9+x-9)=0`
`⇔(x+3)(x²-2x)=0`
`⇔x(x+3)(x-2)=0`
`(1)x=0`
`(2)x+3=0⇔x=-3`
`(3)x-2=0⇔x=2`
vậy `x=0` hoặc `x=-3` hoặc `x=2`
