Phân tích các đa thức sau thành nhân tử:
a) 4x2- 4xy+ y2
b) 9x3-9x2y - 4x + 4y
c) x2+ 2 + 3(x2-2)
Phân tích các đa thức sau thành nhân tử:
a/ x2 – 3x – 4xy + 12y b/ x3 – 4x2 + 4x -1
c/ x – y – ax + ay d/ x2 – 4 + ( x + 2)2
e/x3 + x2y – x2z – xyz f/ x2 – y2 – 2x – 2y
a: \(=x\left(x-3\right)-4y\left(x-3\right)\)
=(x-3)(x-4y)
d: \(=\left(x-2\right)\left(x+2\right)+\left(x+2\right)^2\)
\(=\left(x+2\right)\left(x-2+x+2\right)\)
=2x(x+2)
\(a,=x\left(x-3\right)-4y\left(x-3\right)=\left(x-4y\right)\left(x-3\right)\\ b,=\left(x-1\right)\left(x^2+x+1\right)-4x\left(x-1\right)=\left(x-1\right)\left(x^2-3x+1\right)\\ c,=\left(x-y\right)\left(1-a\right)\\ d,=\left(x-2\right)\left(x-2+x+2\right)=2x\left(x-2\right)\\ e,=x^2\left(x+y\right)-xz\left(x+y\right)=x\left(x-z\right)\left(x+y\right)\\ f,=\left(x-y-2\right)\left(x+y\right)\)
Phân tích các đa thức sau thành nhân tử:
a/ x( 3- x) – x + 3 b/ 3x2 – 5x – 3xy + 5y c/ x2 – xy – 10x + 10y
d/ 2xy+ x2 + y2 - 16 e/ x2 – y2 – 4x – 4y f/ 9 – 4x2 + 4xy – y2
g/ y3 – 2xy2 + x2y h/ x3 – 3x2 – 4x + 12 i/ x( x- y) + x2 – y2
a: \(=\left(3-x\right)\left(x+1\right)\)
b: \(=3x\left(x-y\right)-5\left(x-y\right)\)
=(x-y)(3x-5)
c: \(=x\left(x-y\right)-10\left(x-y\right)\)
\(=\left(x-y\right)\left(x-10\right)\)
a) \(=x\left(3-x\right)+\left(3-x\right)=\left(3-x\right)\left(x+3\right)\)
b) \(=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
c) \(=x\left(x-y\right)-10\left(x-y\right)=\left(x-y\right)\left(x-10\right)\)
d) \(=\left(x+y\right)^2-16=\left(x+y-4\right)\left(x+y+4\right)\)
e) \(=\left(x-y\right)\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(x-y-4\right)\)
f) \(=9-\left(4x^2-4xy+y^2\right)=9-\left(2x-y\right)^2=\left(3-2x+y\right)\left(3+2x-y\right)\)
g) \(=y\left(y^2-2xy+x^2-y\right)\)
h) \(=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
i) \(=x\left(x-y\right)+\left(x-y\right)\left(x+y\right)=\left(x-y\right)\left(2x+y\right)\)
phân tích các đa thức sau thành nhân tử
a, 3x2 - 6
b, x2 - 2x +1 - y2
c, 9x3 - 9x2y - 4x + 4y
d, x3 - 2x2 - 8x
giúp emm
\(a,=3\left(x^2-2\right)\\ b,=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\\ c,=9x^2\left(x-y\right)-4\left(x-y\right)=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\\ d,=x\left(x^2-2x-8\right)=x\left(x^2+2x-4x-8\right)=x\left(x+2\right)\left(x-4\right)\)
Phân tích đa thức thành nhân tử:
a)x2-4xy+x-4y
b)x2-6xy+9y2-4
c)x3-4x2-12x+27
a) = (x - 4y)(x + 1)
b) = (x - 3y)^2 - 2^2
= (x - 3y - 2)(x - 3y + 2)
c) = x^2(x + 3) - 7x(x + 3) + 9(x + 3)
= (x + 3)(x^2 - 7x + 9)
a: \(x^2-4xy+x-4y\)
\(=x\left(x-4y\right)+\left(x-4y\right)\)
\(=\left(x-4y\right)\left(x+1\right)\)
b: \(x^2-6xy+9y^2-4\)
\(=\left(x-3y\right)^2-4\)
\(=\left(x-3y-2\right)\left(x-3y+2\right)\)
Phân tích các đa thức sau thành nhân tử:
a) A= \(x^3\)y - 12xy - x2y
b)B= 4x2 - 3y2 - 4xy - 2x + 3y
c)C= (x+1)(x+2)(x+3)(x+4) - 120
d)D= x5 - x4 + x2 - 1
a: \(A=x^3y-12xy-x^2y\)
\(=xy\cdot x^2-xy\cdot12-xy\cdot x\)
\(=xy\left(x^2-x-12\right)\)
\(=xy\left(x^2-4x+3x-12\right)\)
\(=xy\left[x\left(x-4\right)+3\left(x-4\right)\right]\)
\(=xy\left(x-4\right)\left(x+3\right)\)
c: \(C=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-120\)
=(x+1)(x+4)(x+2)(x+3)-120
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-120\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24-120\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)-96\)
\(=\left(x^2+5x+16\right)\left(x^2+5x-6\right)\)
\(=\left(x^2+5x+16\right)\left(x+6\right)\left(x-1\right)\)
d: \(D=x^5-x^4+x^2-1\)
\(=\left(x^5-x^4\right)+\left(x^2-1\right)\)
\(=x^4\left(x-1\right)+\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^4+x+1\right)\)
Phân tích các đa thức sau thành nhân tử [ làm các bước luôn ạ, chứ đừng có ra kết quả ko thoi ạ ( - _ - ) ]
a/ 3x2 - 6x
b/ x2 - 2x + 1 - y2
c/ 9x3 - 9x2y - 4x + 4y
d/ x3 - 2x2 - 8x
a) \(3x^2-6x\)
\(=3x\left(x-2\right)\)
b) \(x^2-2x+1-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-y-1\right)\left(x+y-1\right)\)
c) \(9x^3-9x^2y-4x+4y\)
\(=\left(9x^3-9x^2y\right)-\left(4x-4y\right)\)
\(=9x^2\left(x-y\right)-4\left(x-y\right)\)
\(=\left(x-y\right)\left(9x^2-4\right)\)
\(=\left(x-y\right)\left(3x-2\right)\left(3x+2\right)\)
a)\(3x^2-6x=3x\left(x-2\right)\)
b)\(x^2-2x+1-y^2=\left(x^2-2x+1\right)-y^2=\left(x-1\right)^2-y^2=\left[\left(x-1\right)-y\right]\left[\left(x-1+y\right)\right]=\left(x-1-y\right)\left(x-1+y\right)\)
c)\(9x^3-9x^2y-4x+4y=\left(9x^3-9x^2y\right)-\left(4x-4y\right)=9x^2\left(x-y\right)-4\left(x-y\right)=\left(x-y\right)\left(9x^2-4\right)=\left(x-y\right)\left[\left(3x\right)^2-2^2\right]=\left(x-y\right)\left(3x-2\right)\left(3x+2\right)\)
d)\(x^3-2x^2-8x=x\left(x^2-2x-8\right)\)
Phân tích các đa thức sau thành nhân tử:
a) 4x2-4x+1
b)16y3-2x3-6x(x+1)-2
c)x2-6xy-25z2+9y2
\(a,4x^2-4x+1\\ =\left(2x\right)^2-2.2x+1^2=\left(2x-1\right)^2\\ c,x^2-6xy-25z^2+9y^2\\ =\left(x^2-2.x.3y+9y^2\right)-\left(5z\right)^2\\ =\left(x-3y\right)^2-\left(5z\right)^2\\ =\left(x-3y-5z\right)\left(x-3y+5z\right)\)
Xem lại đề ý b
Phân tích đa thức thành nhân tử:
a,x2 + xy + 5x + 5y
b,xy - x2 - 3y + 3x
c,2x3 - 6x3 + 18x
d, x2 - 4x - 4y2 + 4
e, x2 - 10x + 9
f, 4x2 - 4x - 3
\(a,=x\left(x+y\right)+5\left(x+y\right)=\left(x+5\right)\left(x+y\right)\\ b,=x\left(y-x\right)-3\left(y-x\right)=\left(x-3\right)\left(y-x\right)\\ c,=18x-4x^3=2x\left(9-2x^2\right)\\ d,=\left(x-2\right)^2-4y^2=\left(x-2y-2\right)\left(x+2y-2\right)\\ e,=x^2-x-9x+9=\left(x-1\right)\left(x-9\right)\\ f,=4x^2-6x+2x-3=\left(2x-3\right)\left(2x+1\right)\)
Phân tích đa thức thành nhân tử:
a) 81x5-x3
b) 9x2y-12xy+4y
c) (5-x)2-16(x-2)2
d) 9x2-y2-21x-7y
e) -y2+8y+9x2-16
f) 5x2-4x-1
g) (x+7)(x+9)-17
h) x(x+2)(x+4)(x+6)+15
a: \(81x^5-x^3\)
\(=x^3\left(81x^2-1\right)\)
\(=x^3\left(9x-1\right)\left(9x+1\right)\)
b: \(9x^2y-12xy+4y\)
\(=y\left(9x^2-12x+4\right)\)
\(=y\left(3x-2\right)^2\)
c: \(\left(5-x\right)^2-16\left(x-2\right)^2\)
\(=\left(x-5\right)^2-\left(4x-8\right)^2\)
\(=\left(x-5-4x+8\right)\left(x-5+4x-8\right)\)
\(=-3\left(x-1\right)\left(5x-13\right)\)
d: Ta có: \(9x^2-y^2-21x-7y\)
\(=\left(3x-y\right)\left(3x+y\right)-7\left(3x+y\right)\)
\(=\left(3x+y\right)\left(3x-y-7\right)\)
e: Ta có: \(-y^2+8y-16+9x^2\)
\(=-\left(y^2-8y+16-9x^2\right)\)
\(=-\left(y-4-3x\right)\left(y-4+3x\right)\)
f: Ta có: \(5x^2-4x-1\)
\(=5x^2-5x+x-1\)
\(=5x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+1\right)\)