Toán Lớp 8: phân tích các đa thức sau thành nhân tử:
a)x^2-y^2+5x-5y
b) 5x^3-5x^2y-10x^2+10y^2
c)x^2+2x+1-9y^2
d)6x^3-12x^2y+6xy^2
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 8: phân tích các đa thức sau thành nhân tử:
a)x^2-y^2+5x-5y
b) 5x^3-5x^2y-10x^2+10y^2
c)x^2+2x+1-9y^2
d)6x^3-12x^2y+6xy^2
Comments ( 2 )
Giải đáp + Lời giải và giải thích chi tiết:
$\text{a, x² – y² + 5x – 5y}$
$\text{=( x² – y² ) + ( 5x – 5y ) }$
$\text{= ( x – y ) ( x + y ) 5 ( x – y ) }$
$\text{= ( x – y )( x + y + 5 ) }$
$\text{b, 5x³ – 5x²y – 10 x² + 10 y²}$
$\text{= ( 5x³ – 5x²y ) – ( 10 x² + 10 y² )}$
$\text{= 5x²( x – y ) – 10 ( x² + y² )}$
$\text{= 5x² ( x – y ) – 10 ( x – y ) ( x + y ) }$
$\text{= ( 5x² – 10 ) ( x – y ) ( x + y ) }$
$\text{= 5 ( x² – 2 ) ( x – y ) ( x + y ) }$
$\text{c, x² + 2x + 1 – 9y²}$
$\text{= ( x² + 2x + 1 ) – 9y²}$
$\text{= ( x + 1 )² – ( 3y )²}$
$\text{= ( x + 1 – 3y ) ( x + 1 + 3y )}$
$\text{d, 6x³ – 12 x²y + 6xy²}$
$\text{= 6x ( x² – 2xy + y² }$
$\text{= 6x ( x – y )²}$
a)
x^2 – y^2 + 5x -5y
= (x^2-y^2) +(5x-5y)
= (x-y)(x+y) + 5 (x-y)
= (x-y)(x+y+5)
b)
5x^3 – 5x^2y – 10x^2 + 10y^2
= (5x^3 – 5x^2y) – (10x^2 -10y^2)
= 5x^2 (x-y) – 10(x^2-y^2)
= 5x^2 (x-y) – 10 (x-y)(x+y)
= 5(x-y) [ x^2 – 2 (x+y)]
= 5 (x-y)(x^2 – 2x -2y)
c)
x^2 + 2x + 1 – 9y^2
= (x^2+2x+1)-9y^2
= (x+1)^2 – (3y)^2
= (x+1-3y)(x+1+3y)
d)
6x^3 – 12x^2y + 6xy^2
= 6x (x^2 – 2xy + y^2)
= 6x (x-y)^2