Bài 1:
`a)7x+21y=7.x+7.3y=7(x+3y)`
`b)2021x(x-7)+5(7-x)`
`=2021x(x-7)+5(-x+7)`
`=2021x(x-7)-5(x-7)`
`=(x-7)(2021x-5)`
`c)x^4+6x³+9x²`
`=(x^2)^2+2.x².3x+(3x)²`
`=(x²+3x)²`
Bài 2:
`a)x²-2xy+y²+3x-3y`
`=(x²-2xy+y²)+(3x-3y)`
`=(x-y)²+3(x-y)`
`=(x-y)(x-y+3)`
`b)x²+x-y²+y`
`=(x²-y²)+(x+y)`
`=(x+y)(x-y)+(x+y)`
`=(x+y)(x-y+1)`
`c)x²+5x+6`
`=x²+2x+3x+6`
`=x(x+2)+3(x+2)`
`=(x+2)(x+3)`
`d)x²-8x+7`
`=x²-7x-x+7`
`=x(x-7)-(x-7)`
`=(x-7)(x-1)`
Bài 3:
`a)3x(x+4)-5(x+4)=0`
`⇔(x+4)(3x-5)=0`
`⇔`\(\left[ \begin{array}{l}x+4=0\\3x-5=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-4\\x=\dfrac{5}{3}\end{array} \right.\)
Vậy `x=-4` hoặc `x=5/3`
`b)x(x-6)-3x+18=0`
`⇔x(x-6)-3(x-6)=0`
`⇔(x-6)(x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-6=0\\x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=6\\x=3\end{array} \right.\)
Vậy `x=6` hoặc `x=3`
Bài 4:
`M=x²+4x+7`
`=x²+4x+4+3`
`=(x²+4x+4)+3`
`=(x²+2.x.2+2²)+3`
`=(x+2)²+3`
Ta có:`(x+2)²≥0` với `∀x`
`⇒(x+2)²+3≥3` với `∀x`
Vậy `GTN``N` của biểu thức `M=3` khi `x+2=0⇔x=-2`
`---------`
Bài 1:
`a)5x-20y=5.x-5.4y=5(x-4y)`
`b)2/3x(y-5)-7(5-y)`
`=2/3x(y-5)-7(-y+5)`
`=2/3x(y-5)+7(y-5)`
`=(y-5)(2/3x+7)`
`c)x^(m+2)+x^m`
`=x^m .x^2+x^m`
`=x^m(x^2+1)`
Bài 2:
`a)x(x-1)+3x-3`
`=x(x-1)+3(x-1)`
`=(x-1)(x+3)`
`b)x²-xy+4x-2y+4`
`=(x²+4x+4)-(xy+2y)`
`=(x²+2.x.2+2²)-y(x+2)`
`=(x+2)²-y(x+2)`
`=(x+2)(x+2-y)`
Bài 3:
`a)3x(x+7)+x+7=0`
`⇔3x(x+7)+(x+7)=0`
`⇔(x+7)(3x+1)=0`
`⇔`\(\left[ \begin{array}{l}x+7=0\\3x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-7\\x=-\dfrac{1}{3}\end{array} \right.\)
Vậy `x=-7` hoặc `x=-1/3`
`b)4x(x-5)-3x+15=0`
`⇔4x(x-5)-3(x-5)=0`
`⇔(x-5)(4x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-5=0\\4x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=5\\x=\dfrac{3}{4}\end{array} \right.\)
Vậy `x=5` hoặc `x=3/4`
