Phân tích các đa thức sau thành nhân tử.
a/ 3a +3b – a^2 – ab
b/ x2^ + x + y^2 – y – 2xy
c/ - x^2 + 7x – 6
d/ 5x^3y – 10x^2y^2 + 5xy^3
e/ 2x2+7x – 15
g/ x^2 -2x+2y-xy
h/ x +4x 16 +4 - 16+4y^2
Bài 1. Phân tích đa thức sau thành nhân tử:
a) 12x²y - 18xy² - 30y³
b) 5x² - 5xy - 10x + 10y
c) a³ - 3a + 3b - b³
d) a⁴ + 6a²b + 9b² - 1
e) 4x² - 25 + (2x + 7)(5 - 2x)
f) x² + 2x - 15
g) x³ - 7x - 6
l) x⁴ + 4
h) x²y + 2xy +y
\(a,=6y\left(2x^2-3xy-5y^2\right)\\ =6y\left(2x^2+2xy-5xy-5y^2\right)\\ =6y\left(x+y\right)\left(2x-5y\right)\\ b,=5x\left(x-y\right)-10\left(x-y\right)=5\left(x-2\right)\left(x-y\right)\\ c,=\left(a-b\right)\left(a^2+ab+b^2\right)-3\left(a-b\right)\\ =\left(a-b\right)\left(a^2+ab+b^2-3\right)\\ d,=\left(a^2+3b\right)^2-1=\left(a^2+3b+1\right)\left(a^2+3b-1\right)\\ e,=\left(2x-5\right)\left(2x+5\right)-\left(2x+7\right)\left(2x-5\right)\\ =\left(2x-5\right)\left(2x+5-2x-7\right)\\ =-2\left(2x-5\right)\\ f,=x^2+5x-3x-15=\left(x+5\right)\left(x-3\right)\\ g,=x^3-x-6x-6\\ =x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\\ =\left(x+1\right)\left(x^2-x-6\right)\\ =\left(x+1\right)\left(x^2-3x+2x-6\right)\\ =\left(x+1\right)\left(x-3\right)\left(x+2\right)\\ l,=x^4+4x^2+4-4x^2\\ =\left(x^2+2\right)^2-4x^2=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\\ h,=y\left(x^2+2x+1\right)=y\left(x+1\right)^2\)
Phân tính đa thức thành nhân tử : mọi người giúp mình nha làm đc bài nào thì làm
a) 2xy-x^2-y^2+7x-7y
b)2xy-x^2-y^2+16
c)3x^2+5x+2
d)4x^2-7x+3
e)a^3+3a^2+2a
f)x^2y^2+x^4-2x^3y-9x^2
a)5x^3y-10x^2y^2+5xy^3
b)2x^2+7x-15
c)x^2-2x=2y-xy
d)x^2+4xy-16+4y^2
c/\(x^2-2x=2y-xy\)
\(x^2-2x+xy-2y=0\)
\(x\left(x-2\right)+y\left(x-2\right)=0\)
\(\left(x+y\right)\left(x-2\right)=0\)
d/\(x^2+4xy-16+4y^2\)
\(=\left(x^2+4xy+4y^2\right)-16\)
\(=\left(x+2y\right)^2-4^2\)
\(=\left(x+2y-4\right)\left(x+2y+4\right)\)
b/\(2x^2+7x-15\)
\(=2x^2+10x-3x-15\)
\(=\left(2x^2+10x\right)-\left(3x+15\right)\)
\(=2x\left(x+5\right)-3\left(x+5\right)\)
\(=\left(2x-3\right)\left(x+5\right)\)
Phân tích đa thức thành nhân tử:
a) x - 2y + x^2- 4y^2
b) x^2 - 4x^2y^2 + y^2 + 2xy
c) x^6 - x^4 +2x^3 + 2x^2
d) x^3 + 3x^2 + 3x +1 - 8y^3
a) Ta có: \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left(x+2y+1\right)\)
b) Ta có: \(x^2+2xy+y^2-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
c) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
\(=x^2\left(x+1\right)\left[x^2\left(x-1\right)+2\right]\)
\(=x^2\left(x+1\right)\cdot\left(x^3-x^2+2\right)\)
d) Ta có: \(x^3+3x^2+3x+1-8y^3\)
\(=\left(x+1\right)^3-\left(2y\right)^3\)
\(=\left(x+1-2y\right)\left[\left(x+1\right)^2+2y\left(x+1\right)+4y^2\right]\)
\(=\left(x-2y+1\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)
Phân tích đa thức thành nhân tử:
a) x - 2y + x^2 - 4y^2
b) x^2 - 4x^2y^2 + y^2 + 2xy
c) x^6 - x^4 + 2x^3 + 2x^2
d) x^3 + 3x^2 + 3x + 1 - 8y^3
a, \(x-2y+x^2-4y^2=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)=\left(x-2y\right)\left(1+x+2y\right)\)
b, \(x^2-4x^2y^2+y^2+2xy=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
c, \(x^6-x^4+2x^3+2x^2=x^6+2x^3+1-x^4+2x^2-1\)
\(=\left(x^3+1\right)^2-\left(x^2-1\right)^2=\left(x^3-x^2+2\right)\left(x^3+x^2\right)\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
d, \(x^3+3x^2+3x+1-8y^3=\left(x+1\right)^3-\left(2y\right)^3=\left(x+1-2y\right)\left(x+1+2y\right)\)
a) Ta có: \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left(1+x+2y\right)\)
b: Ta có: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
Phân tích đa thức sau thành nhân tử
a. 27a^2b^2+18ab+3
b.5x^2-y+5xy-x
c.2x^3y^2-8x^3-12x^2y-6xy^2-y^3+x^2y^3
Bài 1: Phân tích đa thức thành nhân tử
1. 5x-10-xy+2y
2.2x^2+2y^2-4xy-xz+yz
3.5x^2y-10xy^2
4.3x^2-6xy+3y^2-12z^2
5.x^2+4xy-16+4y^2
6.7x-6x^2-2
7.(2x+y)^2+x(2x+y)
8.x(x-y)+5x-5y
9.x^2-y^2+2x+1
10.x^3-9x
11.xy-2y+x-2
12.x^3-3x^2-4x+12
13.3x-x^2-2xy+3y-y^2
\(1,=\left(x-2\right)\left(5-y\right)\\ 2,=2\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(2x-2y-z\right)\\ 3,=5xy\left(x-2y\right)\\ 4,=3\left(x^2-2xy+y^2-4z^2\right)=3\left[\left(x-y\right)^2-4z^2\right]\\ =3\left(x-y-2z\right)\left(x-y+2z\right)\\ 5,=\left(x+2y\right)^2-16=\left(x+2y-4\right)\left(x+2y+4\right)\\ 6,=-\left(6x^2-3x-4x+2\right)=-\left(2x-1\right)\left(3x-2\right)\\ 7,=\left(2x+y\right)\left(2x+y+x\right)=\left(2x+y\right)\left(3x+y\right)\\ 8,=\left(x-y\right)\left(x+5\right)\\ 9,=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\\ 10,=\left(x^2-9\right)x=x\left(x-3\right)\left(x+3\right)\\ 11,=\left(x-2\right)\left(y+1\right)\\ 12,=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\\ 13,=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)
phân tích đa thức thành nhân tử
a) 2x^2 - 2y^2
b) x^2 -4x + 4
c) x^2 + 2x + 1 - y^2
d) x^2 - 4x
e) x^2 + 10x + 25
g) x^2 -2xy + y ^2 - 9
h) 2x^2 - 2
i) 5x^2 - 5xy + 9x - 9y
k) y^2 - 4y + 4 - x^2
l)x^2 - 16
m) 3x^2 -3xy +2x - 2y
o) 3x^4 - 6x ^3 + 3x^2
a) \(2x^2-2y^2\)
\(=2\left(x^2-y^2\right)\)
\(=2\left(x-y\right)\left(x+y\right)\)
b) \(x^2-4x+4\)
\(=x^2-2\cdot x\cdot2+2^2\)
\(=\left(x-2\right)^2\)
c) \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x+y+1\right)\)
d) \(x^2-4x\)
\(=x\left(x-4\right)\)
e) \(x^2+10x+25\)
\(=x^2+2\cdot x\cdot5+5^2\)
\(=\left(x+5\right)^2\)
g) \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
h) \(2x^2-2\)
\(=2\left(x^2-1\right)\)
\(=2\left(x-1\right)\left(x+1\right)\)
i) \(5x^2-5xy+9x-9y\)
\(=5x\left(x-y\right)+9\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+9\right)\)
k) \(y^2-4y+4-x^2\)
\(=\left(y-2\right)^2-x^2\)
\(=\left(y-x-2\right)\left(y+x-2\right)\)
l) \(x^2-16\)
\(=x^2-4^2\)
\(=\left(x-4\right)\left(x+4\right)\)
m) \(3x^2-3xy+2x-2y\)
\(=3x\left(x-y\right)+2\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+2\right)\)
o) \(3x^4-6x^3+3x^2\)
\(=3x^2\left(x^2-2x+1\right)\)
\(=3x^2\left(x-1\right)^2\)
a) 2x2 - 2y2
= (2x - 2y)(2x + 2y)
= 4(x - y)(x + y)
b) x2 - 4x + 4
= (x - 2)2
c) x2 + 2x + 1 - y2
= (x + 1)2 - y2
= (x + 1 - y)(x + 1 + y)
d) x2 - 4x
= x(x - 4)
e) x2 +10x + 25
= (x + 5)2
g) x2 - 2xy + y2 - 9
= (x - y)2 - 32
= (x - y - 3)(x - y + 3)
h) 2x2 - 2
= 2(x2 - 1)
= 2(x - 1)(x + 1)
i) 5x2 - 5xy + 9x - 9y
= 5x(x - y) + 9(x- y)
= (5x + 9)(x - y)
k) y2 - 4y + 4 - x2
= (y - 2)2 - x2
= (y - 2 - x)(y - 2 + x)
l) x2 - 16
= x2 - 42
= (x - 4)(x + 4)
m) 3x2 - 3xy + 2x -2y
= 3x(x - y) +2(x-y)
= (3x + 2)(x - y)
o) 3x4 - 6x3 + 3x2
= 3x4 - 3x3 - 3x3 + 3x2
= 3x3(x - 1) - 3x2(x - 1)
= (3x3 - 3x2)(x - 1)
= 3x2(x - 1)(x - 1)
= 3x2.(x - 1)2
Bài 1: Tính 1) 7x^2 ( x^2 - 5x +1 ) 2) ( 2x - 3 ) ( x + 7 ) Bài 2 : phân tích đa thức thành nhân tử 1) 4x^2y - 8x^3y^2 2) 2x - 4y - ax + 2ay
Bài 1:
a) \(7x^2\left(x^2-5x+1\right)=7x^4-35x^3+7x^2\)
b) \(\left(2x-3\right)\left(x+7\right)=2x^2+11x-21\)
Bài 2:
a) \(4x^2y-8x^3y^2=4x^2y\left(1-2xy\right)\)
b) \(2x-4y-ax+2ay=x\left(2-a\right)-2y\left(2-a\right)=\left(2-a\right)\left(x-2y\right)\)