Phân tích đa thức sau thành nhân tử
1. x mũ 2 - 4xy + 4y mũ 2 + xz - 2yz
2, (x - y) mũ 3 + (x+y) mũ 3
Phân tích đa thức sau thành nhân tử
1. x mũ 2 - 4xy + 4y mũ 2 + xz - 2yz
2, (x - y) mũ 3 + (x+y) mũ 3
1) \(x^2-4xy+4y^2+xz-2yz\)
\(=\left(x^2-4xy+4y^2\right)+\left(xz-2yz\right)\)
\(=\left(x-2y\right)^2+z\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-2y+z\right)\)
2) \(\left(x-y\right)^3+\left(x+y\right)^3\)
\(=\left[\left(x-y\right)+\left(x+y\right)\right]\left[\left(x-y\right)^2-\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\right]\)
\(=\left(x-y+x+y\right)\left(x^2-2xy+y^2-x^2+y^2+x^2+2xy+y^2\right)\)
\(=2x\left(x^2+3y^2\right)\)
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 đa thức thành nhân tử: ax^2 + a^2y - 7x - 7y
giúp mình với nha
X(y-1)-y(y-1)
5x(x-2)-x+2
4x(x+1)-8x-8
Phân tích đa thức thành nhân tử
\(x\left(y-1\right)-y\left(y-1\right)\)
\(=\left(y-1\right)\left(x-y\right)\)
_________________
\(5x\left(x-2\right)-x+2\)
\(=5x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(5x-1\right)\)
_________________
\(5x\left(x+1\right)-8x-8\)
\(=5x\left(x+1\right)-\left(8x+8\right)\)
\(=5x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(5x-8\right)\)
5:
\(=4x^2-12x-x^2+10x-25-3\left(x^2+2x+1\right)+\left(2x+2\right)^2-4x^2+5\)
\(=-2x-20-x^2-3x^2-6x-3+4x^2+8x+4\)
=-20-3+4
=-23+4=-27
6:
\(=\left(2x-3\right)\left(x^2-4\right)-2\left(x^3+9x^2+27x+27\right)-x^3+12x^2-48x+64+x^3-27+9x^2+110x\)
\(=2x^3-8x-3x^2+12-2x^3-18x^2-54x-54+21x^2+62x+37\)
=12+37
=49
1: \(A=3\left(x^2-2x+1\right)-x^2-2x-1+2x^2-18-\left(2x+3\right)^2+20x-5\)
\(=3x^2-6x+3+x^2+18x-24-4x^2-12x-9\)
=3-24-9=-30
2: \(B=5x\left(x^2-49\right)-x\left(4x^2-4x+1\right)-x^3-4x^2+246x-175\)
\(=5x^3-245x-4x^3+4x^2-x-x^3-4x^2+246x-175\)
=-175
3: \(C=-2x\left(9x^2+12x+4\right)+16x^2+8x+1+2x^3+22x-4-5+x\)
\(=-18x^3-24x^2-8x+2x^3+16x^2+31x-8\)
=-16x^3-8x^2+23x-8
4:
\(=25x^2-20x+4-36x^2-12x-1+11x^2-44-16\left(3-2x\right)\)
\(=-32x-41-48+32x=-89\)
a)x^2+5x+6
b5x^2+5xy-x-y
c,7x-6x^2-2
phân tích thành nhân tử bằng 4 cách khác nhau
a: =x^2+2x+3x+6
=(x+2)(x+3)
b: =5x(x+y)-(x+y)
=(x+y)(5x-1)
c: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
phân tích thành nhân tử
9x2-3x-2y-4y2
Từ vựngHán tựDịchĐang tìm kiếm ... Tiếng Anh Từ điển JP9x^2-4y^2-3x-2y
=(3x-2y)(3x+2y)-(3x+2y)
=(3x+2y)(3x-2y-1)
Phân tích đa thức thành nhân tử
b. 25-x2=14xy-49y2
c. x5+x4+1
Mọi người giúp mình với ạ
b) \(25-x^2+14xy-49y^2\)
\(=25-\left(x^2-14xy+49y^2\right)\)
\(=25-\left[x^2-2\cdot7y\cdot x+\left(7y\right)^2\right]\)
\(=25-\left(x-7y\right)^2\)
\(=5^2-\left(x-7y\right)^2\)
\(=\left[5-\left(x-7y\right)\right]\left[5+\left(x-7y\right)\right]\)
\(=\left(5-x+7y\right)\left(5+x-7y\right)\)
c) \(x^5+x^4+1\)
\(=x^5+x^4+1+x^3-x^3\)
\(=\left(x^5+x^4+x^3\right)+\left(1-x^3\right)\)
\(=x^3\left(x^2+x+1\right)+\left(1-x\right)\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x^3+\left(1-x\right)\right]\)
\(=\left(x^2+x+1\right)\left(x^3+1-x\right)\)
b: 25-x^2+14xy-49y^2
=25-(x-7y)^2
=(5-x+7y)(5+x-7y)
c: =x^5+x^4+x^3+1-x^3
=x^3(x^2+x+1)+(1-x)(x^2+x+1)
=(x^2+x+1)(x^3+1-x)
3x3-24 giúp mik với ạ
\(3x^3-24\)
\(=3\left(\left(x-2\right)x^2+2\left(x^2-2x\right)+4\left(x-2\right)\right)\)
\(=3\left(x-2\right)\left(x^2+2x+4\right)\)
\(3x^3-24\\ =3\left(x^3-8\right)\\ =3\left(x^3-2^3\right)\\ =3\left(x-2\right)\left(x^2+2x+4\right)\)