Phân tích các đa thức sau thành nhân tử:
a)x^2 + 9x + 20 b)x^4 - 5x^2 + 4 c)x^4 + 4 d)x(x + 1)(x + 2)(x + 3) + 1
Phân tích các đa thức sau thành nhân tử:
a) \(4{x^3} - 16x\)
b) \({x^4} - {y^4}\)
c) \(x{y^2} + {x^2}y + \dfrac{1}{4}{y^3}\)
d) \({x^2} + 2x - {y^2} + 1\)
`a, 4x^3 - 16x = 4x(x^2-4) = 4x(x-2)(x+2)`
`b, x^4 - y^4 = (x^2-y^2)(x^2+y^2) = (x-y)(x+y)(x^2+y^2)`
`c, xy^2 + x^2y + 1/4y^3`
`= y(xy + x^2 + 1/4y^2)`
`d, x^2 + 2x - y^2 + 1 = (x+1)^2 - y^2`
`= (x+1+y)(x+1-y)`
Phân tích các đa thức sau thành nhân tử:
a) \({\left( {x - 1} \right)^2} - 4\)
b) \(4{x^2} + 12x + 9\)
c) \({x^3} - 8{y^6}\)
d) \({x^5} - {x^3} - {x^2} + 1\)
e) \( - 4{x^3} + 4{x^2} + x - 1\)
f) \(8{x^3} + 12{x^2} + 6x + 1\)
\(a,\left(x-1\right)^2-2^2=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\\ b,=\left(2x\right)^2+2.2x.3+3^2\\ =\left(2x+3\right)^2\\ c,=x^3-\left(2y\right)^3\\ =\left(x-2y\right)\left(x^2+2xy+4y^2\right)\\ d,=x^3\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^3-1\right)\left(x^2-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\)
\(e,=-4x^2\left(x-1\right)+\left(x-1\right)\\ =\left(1-4x^2\right)\left(x-1\right)\\ =\left(1-2x\right)\left(1+2x\right)\left(x-1\right)\)
\(f,=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1^2+1^3\\ =\left(2x+1\right)^3\)
Phân tích đa thức thành nhân tử:
a) y ( x - z ) - 8 ( z - x )
b) x^2 - 5x + 6
c) x^4 + 9x^2 - 10
Giúp mình với ạ plss
a: =(x-z)(y+8)
b; =x^2-2x-3x+6
=(x-2)(x-3)
c: =x^4+10x^2-x^2-10
=(x^2+10)(x^2-1)
=(x^2+10)(x-1)(x+1)
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 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
=
hãy phân tích các đa thức sau thành nhân tử:
a) 2/5x(y-1)-2/5y(y-1)
b) x^3 + 2x^2y+ xy^2 - 9x
a: \(=\dfrac{2}{5}\left(xy-x-y^2+1\right)\)
\(=\dfrac{2}{5}\left[x\left(y-1\right)-\left(y-1\right)\left(y+1\right)\right]\)
\(=\dfrac{2}{5}\left(y-1\right)\left(x-y-1\right)\)
b: \(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
phân tích đa thức sau thành nhân tử:
a) x^8 + x^4 -2
b)x^2n + 5x^n - 24, n thuộc N*
c) (x^2 + x)^2 -2(x^2 +x ) - 15
(x^2 + x +1)(x^2 +x +2) -12
a) \(x^8+x^4-2\)
\(=x^8+x^7+x^6+x^5+2x^4+2x^3+2x^2+2x-x^7-x^6-x^5-x^4-2x^3-2x^2-2x-2\)
\(=x\left(x^7+x^6+x^5+x^4+2x^3+2x^2+2x+2\right)-\left(x^7+x^6+x^5+x^4+2x^3+2x^2+2x+2\right)\)
\(=\left(x-1\right)\left(x^7+x^6+x^5+x^4+2x^3+2x^2+2x+2\right)\)
\(=\left(x-1\right)\left[x^4\left(x^3+x^2+x+1\right)+2\left(x^3+x^2+x+1\right)\right]\)
\(=\left(x-1\right)\left(x^4+2\right)\left(x^3+x^2+x+1\right)\)
\(=\left(x-1\right)\left(x^2+2\right)\left[x^2\left(x+1\right)+\left(x+1\right)\right]\)
\(=\left(x-1\right)\left(x^2+1\right)\left(x^2+1\right)\left(x+1\right)\)
c) \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=x^4+2x^3+x^2-2x^2-2x-15\)
\(=x^4+2x^3-x^2-2x-15\)
\(=x^4+x^3+3x^2+x^3+x^2+3x-5x^2-5x-15\)
\(=x^2\left(x^2+x+3\right)+x\left(x^2+x+3\right)-5\left(x^2+x+3\right)\)
\(=\left(x^2+x+3\right)\left(x^2+x-5\right)\)
d) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(=x^4+2x^3+2x^2+x^2+2x+x^2+x+2-12\)
\(=x^4+2x^3+4x^2+3x-10\)
\(=x^4+3x^3+7x^2+10x-x^3-3x^2-7x-10\)
\(=x\left(x^3+3x^2+7x+10\right)-\left(x^3+3x^2+7x+10\right)\)
\(=\left(x-1\right)\left(x^3+3x^2+7x+10\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+x^2+2x+5x+10\right)\)
\(=\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+5\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+5\right)\)
Phân tích các đa thức sau thành nhân tử:
a) \(9{x^2} - 16\) b) \(4{x^2} - 12xy + 9{y^2}\) c) \({t^3} - 8\) d) \(2a{x^3}{y^3} + 2a\)
`a, 9x^2 - 16 = (3x+4)(3x-4)`
`b, 4x^2 - 12xy + 9y^2 = (2x-3y)^2`
`c, t^3-8 = (t-2)(t^2 - 2t + 4)`
`d, 2ax^3y^3 + 2a = 2a(x^3y^3 + 1) = 2a(xy+1)(x^2y^2 - xy + 1)`
a) \(\left(9x^2-16\right)=\left(3x-4\right)\left(3x+4\right)\)
b) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)
c) \(t^3-8=\left(t-2\right)\left(t^2+2t+4\right)\)
d) \(2ax^3y^3+2a=2a\left(x^3y^3+1\right)\)
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) \(\left(x-y+4\right)^2-\left(2x+3y-1\right)\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)