Phân tích đa thức thành nhân tử
a) \(x^2+3ab\left(2-3ab\right)-10xy-1+25y^2\)
b)\(a^5+a^4+a^3+a^2+a+1\)
c)\(x^3-1+5x^2-5+3x-3\)
phân tích các đa thức sau thành nhân tử
x2+3ab(2-3ab)-10xy-1+25y2
phân tích các đa thức sau thành nhân tử
x2 + 3ab (2-3ab) - 10xy - 1 + 25y2
Phân tích các đa thức sau thành nhân tử:
x2+3ab(2-3ab)-10xy-1+25y2
4(x2-y2)-8(x-yz)-4(z2+1)
x3+y3+z3-3xyz
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 các đa thức sau thành nhân tử:
\(A=4x^2+6x\). \(B=\left(2x+3\right)^2-x\left(2x+3\right)\). \(C=\left(9x^2-1\right)-\left(3x-1\right)^2\).
\(D=x^3-16x\). \(E=4x^2-25y^2\). \(G=\left(2x+3\right)^2-\left(2x-3\right)^2\).
\(A=4x^2+6x=2x\left(2x+3\right)\)
\(B=\left(2x+3\right)^2-x\left(2x+3\right)=\left(2x+3\right)\left(2x+3-x\right)=\left(2x+3\right)\left(x+3\right)\)
\(C=\left(9x^2-1\right)-\left(3x-1\right)^2=\left(3x-1\right)\left(3x+1\right)-\left(3x-1\right)^2=\left(3x-1\right)\left(3x+1-3x+1\right)=2\left(3x+1\right)\)
\(D=x^3-16x=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\)
\(E=4x^2-25y^2=\left(2x-5y\right)\left(2x+5y\right)\)
\(G=\left(2x+3\right)^2-\left(2x-3\right)^2=\left(2x+3-2x+3\right)\left(2x+3+3x-3\right)=6.4x=24x\)
\(A=2x\left(2x+3\right)\\ B=\left(2x+3\right)\left(2x+3-x\right)=\left(2x+3\right)\left(x+3\right)\\ C=\left(3x-1\right)\left(3x+1\right)-\left(3x-1\right)^2\\ =\left(3x-1\right)\left(3x+1-3x+1\right)\\ =2\left(3x-1\right)\\ D=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\\ E=\left(2x-5y\right)\left(2x+5y\right)\\ G=\left(2x+3-2x+3\right)\left(2x+3+2x-3\right)\\ =24x\)
1/ phân tích đa thức thành nhân tử:
a) 7x-6x2-2
b) 2x2+3x-5
c) 16x-5x2-3
2/ Cho a+b+c=0. Chứng minh a3+b3+c3=3ab
1,
\(a,7x-6x^2-2=-6x^2+7x-2=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)=\left(2x-1\right)\left(2-3x\right)\)
\(b,2x^2+3x-5=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
\(c,16x-5x^2-3=-5x^2+x+15x-3\)
\(=-x\left(5x-1\right)+3\left(5x-1\right)=\left(5x-1\right)\left(3-x\right)\)
2,
\(a+b+c=0=>a+b=-c=>\left(a+b\right)^3=\left(-c\right)^3\)
\(=>a^3+b^3+3a^2b+3ab^2=-c^3\)
\(=>a^3+b^3+c^3=-3ab\left(a+b\right)\)
\(=>a^3+b^3+c^3=-3ab\left(-c\right)=3abc\)(vì a+b=-c)
\(2x^2+3x-5\)
\(=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(2x+5\right)\)
PHÂN TÍCH CÁC ĐA THỨC SAU THÀNH NHÂN TỬ:
a) \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right).\)
b) \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)
c) \(x^3-1+5x^2-5+3x-3\)
d) \(a^5+a^4+a^3+a^2+a+1\)
e) \(x^3-3x^2+3x-1-y^3\)
f) \(5x^3-3x^2y-45xy^2+27y^3\)
g) \(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)
Đây, bản full đây thím, tớ thực sự đã kiên nhẫn lắm đấy ...
a)\(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)=4\left(x^2-y^2-2x+2ay-a^2+1\right)\)
\(=4\left[\left(x^2-2x+1\right)-\left(a^2-2ay+y^2\right)\right]\)
\(=4\left[\left(x-1\right)^2-\left(a-y\right)^2\right]\)
\(=4\left(x-1-a+y\right)\left(x-1+a-y\right)\)
b)\(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1\right)-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)
\(=\left(x+y-1\right)\left(x^2-xy+y^2+x+y+1\right)\)
c)\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+\left(x-1\right)\left(5x+5\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)\)
\(=\left(x-1\right)\left(x+3\right)^2\)
d)\(a^5+a^4+a^3+a^2+a+1=a^4\left(a+1\right)+a^2\left(a+1\right)+\left(a+1\right)\)
\(=\left(a+1\right)\left(a^4+a^2+1\right)\)
\(=\left(a+1\right)\left(a^4+2a^2+1-a^2\right)\)
\(=\left(a+1\right)\left[\left(a^2+1\right)^2-a^2\right]\)
\(=\left(a+1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)\)
e)\(x^3-3x^2+3x-1-y^3=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-1-y\right)\left(x^2-2x+1+xy-y+y^2\right)\)
f)\(5x^3-3x^2y-45xy^2+27y^3=5x\left(x^2-9y^2\right)-3y\left(x^2-9y^2\right)\)
\(=\left(x^2-9y^2\right)\left(5x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)\left(5x-3y\right)\)
g)\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)
\(=3\left(a-b+c\right)\left(x+6y\right)^2\)
a/ \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)
\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)
\(=\left(2x-2\right)^2-\left(2y-2a\right)^2=\left(2x-2+2y-2a\right)\left(2x-2-2y+2a\right)\)
b/ \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)=\left(x+y-1\right)\left(x^2+y^2+2xy+x+y+1\right)-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+y^2-xy+x+y+1\right)\)
Giải giúp bạn 2 bài tiêu biểu thôi nha
Phân tích đa thức \(\dfrac{2}{5}x^2+5x^3+x^2y\) thành nhân tử
a. \(x^2\left(\dfrac{2}{5}+5x+y\right)\)
b. \(\dfrac{1}{5}x^2\left(2+25x+5y\right)\)
Cách phân tích nào đúng a hay b và GIẢI THÍCH VÌ SAO?
A. Cách B sai vì 5 : 2/5 thì ko thể nào = 25 đc.
phân tích đa thức thành nhân tử
a, x^3+2x^2-3x-6
b, 2a^2c^2-2abc+bd-acd
c, 5x^2(x-1)-10xy(x-1)-5y^2(1-x)
d, x^5-x^4y -xy^4+y^5
e, x^2-6xy+9y^2-9