Phân tích đa thức thành nhân tử:
a)\(3x^2-9x+30\)
b)\(3x^2-5x-2\)
c)\(x^4+4y^4\)
d)\(x^5+x+1\)
Phân tích đa thức thành các nhân tử:
a)x^2-(a+b)x+ab
b)7x^3-3xyz-21x^2+9z
c)4x+4y-x^2(x+y)
d)y^2+y-x^2+x
e)4x^2-2x-y^2-y
f)9x^2-25y^2-6x+10y
Phân tích đa thức thành nhân tử
a)(5x-4)(4x-5)-(x-3)(x-2)-(5x-4)(3x-2)
b)(5x-4)(4x-5)+(5x-1)(x+4)+3(3x-2)(4-5x)
c)(5x-4)^2+(16-25x^2)+(5x-4)(3x+2)
d)x^4-x^3-x+1
e)x^6-x^4+2x^3+2x^2
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
Phân tích đa thức thành nhân tử a) x^2 -5x+6 b) 3x^2+9x -30 c)3x^2 -5x-2 d) x^3-7x-6 e) x^4+2x^2+6x-9 f) x^2-7xy+10y^2
Phân tích các đa thức sau thành nhân tử:
a) a²-b²-2a+2b.
b) 3x-3y-5x(y-x)
c) x(x+y)²-y(x+y)²+xy-x²
d) (x−y+4)² - (2x+3y-1)²
e) 16-x²+4xy-4y²
f) (x+3)³+(x-3)³
g) 9x²-3xy+y-6x+1
h) x³-3x²y+3xy²-y³-z³
Cần đáp án trc 3h chiều ( 29 /8 )
a: =(a^2-b^2)-(2a-2b)
=(a-b)(a+b)-2(a-b)
=(a-b)(a+b-2)
b: =(3x-3y)+5y(x-y)
=3(x-y)+5y(x-y)
=(x-y)(5y+3)
c: \(=\left(x+y\right)^2\left(x-y\right)+x\left(y-x\right)\)
=(x-y)*(x+y)^2-x(x-y)
=(x-y)[(x+y)^2-x]
d: \(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
=(-x-4y+5)(3x+2y+3)
e: =16-(x^2-4xy+4y^2)
=16-(x-2y)^2
=(4-x+2y)(4+x-2y)
g: =9x^2-6x+1-(3xy-y)
=(3x-1)^2-y(3x-1)
=(3x-1)(3x-y-1)
h: =(x-y)^3-z^3
=(x-y-z)[(x-y)^2+z(x-y)+z^2]
=(x-y-z)(x^2-2xy+y^2+xz-yz+z^2)
a) \(a^2-b^2-2a+2b\)
\(=\left(a^2-b^2\right)-\left(2a-2b\right)\)
\(=\left(a+b\right)\left(a-b\right)-2\left(a-b\right)\)
\(=\left(a-b\right)\left(a+b-2\right)\)
b) \(3x-3y-5x\left(y-x\right)\)
\(=\left(3x-3y\right)+5x\left(x-y\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(5x+3\right)\left(x-y\right)\)
c) \(x\left(x+y\right)^2-y\left(x+y\right)^2+xy-x^2\)
\(=\left(x+y\right)^2\left(x-y\right)+\left(xy-x^2\right)\)
\(=\left(x+y\right)^2\left(x-y\right)-x\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+2xy+y^2-x\right)\)
d) \(\left(x-y+4\right)^2-\left(2x+3y-1\right)\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
Phân tích đa thức thành nhân tử:
a) \(\text{10x+15y}\)
b) \(\text{x(x+y) - 5x - 5y}\)
c) \(3x^3-6x^2+3x\)
d) \(x^2-y^2+2x+1\)
a: =5(2x+3y)
d: =(x+1-y)(x+1+y)
BT1: Phân tích đa thức thành nhân tử bằng phương pháp hạng tử. a, x^2 - 5x + 6 b, 3x^2 + 9x - 30 c, x^2 - 3x + 2 d, 3x^2 - 5x -2
\(a,x^2-5x+6\\=x^2-3x-2x+6\\=x(x-3)-2(x-3)\\=(x-3)(x-2)\\---\\b,3x^2+9x-30\\=3x^2-6x+15x-30\\=3x(x-2)+15(x-2)\\=(x-2)(3x+15)\\=3(x-2)(x+5)\\---\)
\(c,x^2-3x+2\\=x^2-x-2x+2\\=x(x-1)-2(x-1)\\=(x-1)(x-2)\\---\\d,3x^2-5x-2\\=3x^2-6x+x-2\\=3x(x-2)+(x-2)\\=(x-2)(3x+1)\\Toru\)
Phân tích đa thức thành nhân tử:
a, \(x^3+3x^2+3x+1-27z^3\)
b, \(x^2-2xy+y^2-xz+yz\)
c, \(x^4+4x^2-5\)
a.
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)
\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)
b.
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c.
\(=x^4-1+4x^2-4\)
\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) Ta có: \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
b) Ta có: \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
1A. Phân tích các đa thức sau thành nhân tử:
a) x3+2x; b) 3x - 6y;
c) 5(x + 3y)- 15x(x + 3y); d) 3(x-y)- 5x(y-x).
1B. Phân tích các đa thức sau thành nhân tử:
a) 4x2 - 6x; b) x3y - 2x2y2 + 5xy;
c) 2x2(x +1) + 4x(x +1); d) 2 x(y - 1) - 2
y(1 - y).
5 5
2A. Phân tích các đa thức sau thành nhân tử: a) 2(x -1)3 - 5(x -1)2 - (x - 1);
b) x(y - x)3 - y(x - y)2 + xy(x - y);
c) xy(x + y)- 2x - 2y;
d) x(x + y)2 - y(x + y)2 + y2 (x - y).
2B. Phân tích đa thức thành nhân tử: a) 4(2-x)2 + xy - 2y;
b) x(x- y)3 - y(y - x)2 - y2(x - y);
c) x2y-xy2 - 3x + 3y;
d) x(x + y)2 - y(x + y) 2 + xy - x 2 .
1A:
a: \(x^3+2x=x\left(x^2+2\right)\)
b: \(3x-6y=3\left(x-2y\right)\)
c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)
\(=5\left(x+3y\right)\left(1-3x\right)\)
d: \(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+3\right)\)
1A. a. x(x2+2)
b. 3(x-2y)
c. 5(x+3y)(1-3x)
d. (x-y) (3-5x)
1B. a. 2x(2x-3)
b.xy(x2-2xy+5)
c. 2x(x+1)(x+2)
d. 2x(y-1)+2y(y-1)=2(y-1)(x-y)
1B:
a: \(4x^2-6x=2x\left(2x-3\right)\)
b: \(x^3y-2x^2y^2+5xy\)
\(=xy\left(x^2-2xy+5\right)\)
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: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)