a) 8x2 + 4xy - 2x - ay
b) 3a2 - 6ab + 3b2 - 12c2
c) x2 - 2xy + y2 - m2 + 2mn - n2
4/ Ph©n tÝch c¸c ®a thøc sau thµnh nh©n tö:
a) x2 - y2 - 2x + 2y b)2x + 2y - x2 - xy
c) 3a2 - 6ab + 3b2 - 12c2 d)x2 - 25 + y2 + 2xy
e) a2 + 2ab + b2 - ac - bc f)x2 - 2x - 4y2 - 4y g) x2y - x3 - 9y + 9x h)x2(x-1) + 16(1- x)
n) 81x2 - 6yz - 9y2 - z2 m)xz-yz-x2+2xy-y2 p) x2 + 8x + 15 k) x2 - x - 12
l) 81x2 + 4
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)
= (x+y)(2-x)
c,3a2-6ab+3b2-12c2
= 3(a2 - 2ab + b2 - 4c2)
= 3[(a-b)2 - 4c2)
= 3(a-b-2c)(a-b+2c)
d,x2-25+y2+2xy
= (x+y)2 - 25
= (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)
p) x2 + 8x + 15
= x2 + 3x + 5x + 15
= x(x+3) + 5(x+3)
= (x+3)(x+5)
k) x2 - x - 12
= x2 + 3x - 4x - 12
= x(x+3) - 4(x+3)
= (x+3)(x-4)
1. 8x2 + 4xy - 2ax - ay
2. 2xy - x2 - y2 + 16
3. X2 - y2 - 2yz - z2
1 : 8x2+4xy-2ax -ay=4x(2x+y)-a(2x+y)=(2x+y)(4x-a)
2,3 tương tự
PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ
a, 3x(2x - y) + 5y(y - 2x)
b, (x - 5)2 - 9(x + y)2
c, y2 + 2yz + z2 - xy - xz
d, x2 - 9x2y2 + y2 + 2xy
e, x2 - 10x + 24
g, 6x2 + 7x - 5
h, x2 + 4xy - 12y2
k, a4 + 3a2 + 4
a) \(3x\left(2x-y\right)+5y\left(y-2x\right)\)
\(=3x\left(2x-y\right)-5y\left(2x-y\right)\)
\(=\left(3x-5y\right)\left(2x-y\right)\)
b) \(\left(x-5\right)^2-9\left(x+y\right)^2\)
\(=\left(x-5\right)^2-3^2\left(x+y\right)^2\)
\(=\left(x-5\right)^2-\left(3x+3y\right)^2\)
\(=\left(x-5+3x+3y\right)\left(x-5-3x-3y\right)\)
\(=\left(4x+3y-5\right)\left(-2x-3y-5\right)\)
a: \(3x\left(2x-y\right)+5y\left(y-2x\right)=\left(2x-y\right)\left(3x-5y\right)\)
e: \(x^2-10x+24=\left(x-4\right)\left(x-6\right)\)
g) \(6x^2+7x-5\)
=\(6x^2+10x-3x-5\)
=\(\left(6x^2+10x\right)-\left(3x+5\right)\)
=\(2x\left(3x+5\right)-\left(3x+5\right)\)
=\(\left(2x-1\right)\left(3x+5\right)\)
Câu 1:Phân tích đa thức thành nhân tử
a/ –6x2y + xy2
b/10a2c – 90b2c + 30bc2 – 10ac2
c/ax + bc – ac – bx
d/36 – x2 + 4xy – 4y2
e/ m2 + n2 + 4m + 4n + 2mn
f/ 2x2 – 1/2y2
\(a,=xy\left(-6x+y\right)\)
\(b,=10c\left(a^2-9b^2+3bc-ac\right)=10c\left[\left(a-3b\right)\left(a+3b\right)-c\left(a-3b\right)\right]\)
\(=10c\left[\left(a-3b\right)\left(a+3b-c\right)\right]\)
c,\(=a\left(x-c\right)-b\left(x-c\right)=\left(a-b\right)\left(x-c\right)\)
d,\(=-\left(x-2y-6\right)\left(x-2y+6\right)\)
e;\(=m^2+4m+mn+n^2+4n+mn=m\left(m+4+n\right)+n\left(m+4+n\right)\)\(=\left(m+n\right)\left(m+n+4\right)\)
f,\(=\dfrac{1}{2}\left(4x^2-y^2\right)=\dfrac{1}{2}\left(2x-y\right)\left(2x+y\right)\)
Phân tích các đa thức sau thành nhân tử:
a) 5 x 3 - 3 x 2 y - 45x y 2 + 27 y 3 ;
b) 3 x 2 (a - b + c) + 36xy(a - b + c) + 108 y 2 (a - b + c);
c) x 2 -2xy + y 2 - 4 m 2 + 4mn - n 2
a) (5x - 3y)(x - 3y)(x + 3y).
b) 3(a – b + c) ( x + 6 y ) 2 .
c) (x-y-2m + n)(x-y + 2m-n)
a, -x2 + 2x + 3
b, x2 - 2x + 4y2 - 4y + 8 c, -x2 - y2 + xy + 2x + 2y + 4 d, x2 + 5y2 - 4xy - 2y + 2015 e, 2x2 + y2 + 6x + 2y + 2xy + 2018A= -x2+2x+3
=>A= -(x2-2x+3)
=>A= -(x2-2.x.1+1+3-1)
=>A=-[(x-1)2+2]
=>A= -(x+1)2-2
Vì -(x+1)2 ≤0=> A≤-2
Dấu "=" xảy ra khi
-(x+1)2=0 => x=-1
Vây A lớn nhất= -2 khi x= -1
B=x2-2x+4y2-4y+8
=> B= (x2-2x+1)+(4y2-4y+1)+6
=> B=(x-1)2+(2y+1)2+6
=> B lớn nhất=6 khi x=1 và y=-1/2
a) 3x(x+1)-x(3x+2)
b) 2x(x2-5x+6)+(x-1)(x+3)
c) (x2-xy+y2)-(x2+2xy+y2)
d) (2/5xy+x-y)-(3x+4y)-2/5xy
e) 2xy(x2-4xy+4y2)
f) (x+y)(xy+5)
g) (x3-2x2-x+2):(x-1)
h) (2x2+3x-2):(2x-1)
(2x-y)(4x2-4xy+y2)-8x2(x-y)
\(\left(2x-y\right)\left(4x^2-4xy+y^2\right)-8x^2\left(x-y\right)\)
\(=8x^3-y^3-8x^3+8x^2y\)
\(=8x^2y-y^3\)
Phân tích đa thức thành nhân tử:
a) x3 - 2x2 - 2x - 4
b) xy + 1 - x - y
c) x2 - 4xy + 4y2 - 4y
d) 16 - x2 + 2xy - y2
\(a.x^3-2x^2-2x-4\\ =\left(x^3-2x^2\right)-\left(2x-4\right)\\ =x^2\left(x-2\right)-2\left(x-2\right)\\ =\left(x^2-2\right)\left(x-2\right)\)
\(b.xy+1-x-y\\ =\left(xy-x\right)+\left(-y+1\right)\\ =x\left(y-1\right)-\left(y-1\right)\\ =\left(x-1\right)\left(y-1\right)\)
\(c.x^2-4xy+4y^2-4y\\ =\left(x-2y\right)^2-4y\\ =\left(x-2y\right)^2-\left(2y\right)^2\\ =\left(x-2y+2y\right)\left(x-2y-2y\right)\\ =x\left(x-4y\right)\)
\(d.16-x^2+2xy-y^2\\ =4^2-\left(x-y\right)^2\\ =\left(4-x+y\right)\left(4-x-y\right)\)
b: =xy-x-y+1
=x(y-1)-(y-1)
=(x-1)(y-1)
c: =(x-2y)^2-4y
\(=\left(x-2y-2\sqrt{y}\right)\left(x-2y+2\sqrt{y}\right)\)
d: =16-(x^2-2xy+y^2)
=16-(x-y)^2
=(4-x+y)(4+x-y)