Đáp án:
Giải thích các bước giải:
$\text{1/ A=(1-3x)(3-2x)- (6x-2)(x+1)}$
$\text{A= 3-2x-9x+6x²-6x²-6x+2x+2}$
$\text{A= 5-15x= 5(1-3x)}$
$\text{2/}$
$\text{a, (4x-2)²-(2x+1)(8x-1)=0}$
$\text{⇔(2x+1)(2x-1)-(2x+1)(8x-1)=0}$
$\text{⇔(2x+1)(2x-1-8x+1)=0}$
$\text{⇔(2x+1)(-6x)=0}$
⇔$\left[\begin{matrix} 2x+1=0\\ -6x=0\end{matrix}\right.$
⇔$\left[\begin{matrix} 2x=-1\\ x=0\end{matrix}\right.$
⇔\(\left[ \begin{array}{l}x=-1/2\\x=0\end{array} \right.\)
`\text{Vậy ......}`
`\text{b, 15x²- 4x-3=0}`
`\text{⇔15x²-9x+5x-3=0}`
`\text{⇔(15x²+5x)-(9x+3)=0}`
$\text{⇔5x(3x+1)-3(3x+1)=0}$
$\text{(5x-3)(3x+1)=0}$
⇔$\left[\begin{matrix} 5x-3=0\\ 3x+1=0\end{matrix}\right.$
⇔\(\left[ \begin{array}{l}x=3/5\\x=-1/3\end{array} \right.\)
$\text{Vậy ......}$
$\text{3}$
$\text{a, A= x³-4x²+4x}$
⇔$\text{A= x³-2x²-2x²+4x}$
⇔$\text{A=(x³-2x²)-(2x²-4x) }$
⇔$\text{A=x²(x-2)-2x(x-2)}$
⇔$\text{A=(x²-2x)(x-2)}$
⇔$\text{A=x(x-2)(x-2)}$
⇔$\text{A= x(x-2)²}$
$\text{b, B=x²-y²+8y-16}$
⇔$\text{B=x²-(y²-8y+16)}$
⇔$\text{B=x²-(y-4)²}$
⇔$\text{B= (x-y+4)(x+y-4)}$
$\text{c, A=x³+x²-49x-49}$
⇔$\text{A= (x³+x²)-(49x+49)}$
⇔$\text{A=x²(x+1)-49(x+1)}$
⇔$\text{A=(x²-49)(x+1)}$
⇔$\text{A=(x-7)(x+7)(x+1)}$
$\text{d, D=4x²+2x²-25y²+5xy}$
⇔$\text{D= (4x²-25y²)+(2x²+5xy)}$
⇔$\text{D=(2x-5y)(2x+5y)+x(2x+5y)}$
⇔$\text{(2x-5y+x)(2x+5y)}$
$\text{Nâng cao}$
$\text{1}$
$\text{a, A=12x²-5xy-3y²}$
⇔$\text{A=12x²-9xy+4xy-3y²}$
⇔$\text{A=(12x²+4xy)-(9xy+3y²)}$
⇔$\text{A=4x(3x+y)-3y(3x+y)}$
⇔$\text{A=(4x-3y)(3x+y)}$
