Tìm x biết:
8x(x-3)+x-3=0
Phân tích thành nhân tử:
a) x^2-y^2-2x+2y
b) 2x+2y-x^2-xy
c) 3a^2-6ab+3b^2-12c^2
d) x^2-25+y^2+2xy
e) a^2+2ab+b^2-ac-bc
f) x^2-2x-4y^2-4y
g) x^2y-x^3-9y+9x
h) x^2(x-1)+16(1-x)
Tìm x biết:
8x(x-3)+x-3=0
Phân tích thành nhân tử:
a) x^2-y^2-2x+2y
b) 2x+2y-x^2-xy
c) 3a^2-6ab+3b^2-12c^2
d) x^2-25+y^2+2xy
e) a^2+2ab+b^2-ac-bc
f) x^2-2x-4y^2-4y
g) x^2y-x^3-9y+9x
h) x^2(x-1)+16(1-x)
Đáp án:
Giải thích các bước giải:
$1.$
$8x(x-3)+x-3=0$
$(=)(8x+1)(x-3)=0$
\(\left[ \begin{array}{l}8x+1=0\\x-3=0\end{array} \right.\)
=>\(\left[ \begin{array}{l}x=-\dfrac{1}{8}\\x=3\end{array} \right.\)
$2.$
$a,x^2-y^2-2x+2y$
$=(x-y)(x+y)-2(x-y)$
$=(x-y)(x+y-2)$
$b,2x+2y-x^2-xy$
$=2(x+y)-x(x+y)$
$=(2-x)(x+y)$
$c.3a^2-6ab+3b^2-12c^2$
$=3(a^2-2ab+b^2-4c^2)$
$=3[(a-b)^2-4c^2]$
$=3(a-b-2c)(a-b+2c)$
$d.x^2-25+y^2+2xy$
$=(x+2xy+y^2)-25$
$=(x+y)^2-25$
$=(x+y-5)(x+y+5)$
$e,a^2+2ab+b^2-ac-bc$
$=(a+b)^2-c(a+b)$
$=(a+b)(a+b-c)$
$f,x^2-2x-4y^2-4y$
$=(x^2-4y^2)-2(x+2y)$
$=(x-2y)(x+2y)-2(x+2y)$
$=(x+2y)(x-2y-2)$
$g,x^2y-x^3-9y+9x$
$=x^2(y-x)-9(y-x)$
$=(x^2-9)(y-x)$
$=(x-3)(x+3)(y-x)$
$h,x^2(x-1)+16(1-x)$
$=x^2(x-1)-16(x-1)$
$=(x^2-16)(x-1)$
$=(x-4)(x+4)(x-1)$
Đáp án:
Giải thích các bước giải
a) x²-y²-2x+2y= (x-y)(x+y)-2(x-y)= (x-y)(x+y-2)
b)2x+2y-x²-xy= 2(x+y)-x(x+y)= (2-x)(x+y)
c)3a²-6ab+3b²-12c²= 3(a²-2ab+b²)-12c²= 3(a-b)²-12c²= 3[(a-b)²-(2c)²]=3(a-b+2c)(1-b-2c)
d)x²-25+y²+2xy= x²+2xy+y²-5²=(x+y)²-5²=(x+y+5)(x+y-5)
e)a²+2ab+b²-ac-bc= (a+b)²-c(a+b)= (a+b)( a+b-c)
f)x²-2x-4x²-4y= -3x²-2x-4y= -(3x²+2x+4y)
g)x²y-x³-9y+9x= x²(y-x)-9(y-x)= (y-x)(x²-9)
h) x²(x-1)+16(1-x)= x²(x-1)-16(x-1)= (x-1)(x²-16)= (x-1)(x-4)(x+4)
n)81x²-6yz-9y²-z²= (9x)²-[(3y)²+6yz+z²]=(9x)²-(3y+z)²=(9x+3y+z)(9x-3y-z)
m) xz- yz-x²+2xy-y²= z(x-y)-(x²-2xy+y²)= z(x-y)-(x-y)²= (x-y)(z-x+y)