Phân tích đa thức thành nhân tử x^7+x^2+1

\(x^7+x^2+1\)

\(=x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)

Phân tích đa thức thành nhân tử :

\(P=x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

a) 3x-y+3x² - x

\(=3x-1y+3x.x-x.1\)

\(=x.\left(3-y+3x-1\right)\)

Phân tích thành nhân tử :

a) 3x-y+3x²-x

\(P=x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

\(=x^2\left(y-x+x-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

\(=x^2\left(y-x\right)-z^2\left(y-x\right)+x^2\left(x-z\right)-y^2\left(x-z\right)\)

\(=\left(x^2-z^2\right)\left(y-x\right)+\left(x^2-y^2\right)\left(x-z\right)\)

\(=\left(x-z\right)\left(x+z\right)\left(y-x\right)-\left(y-x\right)\left(x-z\right)\left(x+y\right)\)

\(=\left(x-z\right)\left(y-x\right)\left(x+z-x-y\right)\)

\(=\left(x-z\right)\left(y-x\right)\left(z-y\right)\)

Phân tích các đa thức sau thành nhân tử:

* \(x^3-7x+6\)

* \(x^3-9x^2+6x+16\)

* \(x^3-6x^2-x+30\)

* \(2x^3-x^2+5x+3\)

* \(27x^3-27x^2+18x-4\)

* \(x^2+2xy+y^2-x-y-12\)

* \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

* \(4x^4-32x^2+1\)

* \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

* \(64x^4+y^4\)

* \(a^6+a^4+a^2b^2+b^4-b^6\)

* \(x^3+3xy+y^3-1\)

* \(4x^4+4x^3+5x^2+2x+1\)

* \(x^8+x+1\)

* \(x^8+3x^4+4\)

* \(3x^2+22xy+11x+37y+7y^2+10\)

* \(x^4-8x+63\)

* \(\left(x+y+z\right)\left(xy+yz+zx\right)-xyz\)

* \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

* \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

* \(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)

* \(a^3+b^3+c^3-3abc=\left(a+b\right)^3-3ab^2+c^3-3abc\)

* \(\left(a+b+c\right)^3-a^3-b^3-c^3=[\left(a+b\right)c]^3-a^3-b^3-c^3\)

* \(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

\([\) Các bạn làm được bài nài thì làm giúp mk với nha,làm vài câu cũng được\(]\)

Mk mệt quá rồi làm giúp mk với nha

4x³y - 4xy³ - 8xy² - 4xy = 4xy(x² - y² - 2y - 1) = 4xy[x² - (y² + 2y1+ 1²) = 4xy[x² - (y-1)² = 4xy{[x - (y-1)] [x + (y-1)]} = 4xy {[x-y+1][x+y-1]}

a) \(4a^2b^2-\left(a^2+b^2-1\right)^2\)

\(=\left(2ab\right)^2-\left(a^2+b^2-1\right)^2\)

\(=\left(2ab-a^2-b^2+1\right)\left(2ab+a^2+b^2-1\right)\)

\(=\left(1-a^2+2ab-b^2\right)\left(a^2+2ab+b^2-1\right)\)

\(=\left[1-\left(a-b\right)^2\right]\left[\left(a+b\right)^2-1\right]\)

\(=\left(1-a+b\right)\left(1+a-b\right)\left(a+b-1\right)\left(a+b+1\right)\)

b) \(\left(xy+4\right)^2-\left(2x+2y\right)^2\)

\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)

\(1,x^3-7x+6\)

\(=x^3+3x^2-3x^2-9x+2x+6\)

\(=x^2\left(x+3\right)-3x\left(x+3\right)+2\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-3x+2\right)\)

\(=\left(x+3\right)\left(x^2-2x-x+2\right)\)

\(=\left(x+3\right)\left(x-2\right)\left(x-1\right)\)

\(2,x^3-9x^2+6x+16\)

\(=x^3+x^2-10x^2-10x+16x+16\)

\(=x^2\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-10x+16\right)\)

\(=\left(x+1\right)\left(x^2-2x-8x+16\right)\)

\(=\left(x+1\right)\left(x-8\right)\left(x-2\right)\)

a) \(x^4-4x^{3^{ }}+8x+3\)

\(=\left(x^4+x^3\right)-\left(5x^3+5x^2\right)+\left(5x^2+5x\right)+\left(3x+3\right)\)

\(=x^{3^{ }}\left(x+1\right)-5x^{2^{ }}\left(x+1\right)+5x\left(x+1\right)+3\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3-5x^2+5x+3\right)\)

\(=\left(x+1\right)\left[\left(x^3-3x^2\right)-\left(2x^2-6x\right)-\left(x-3\right)\right]\)

\(=\left(x+1\right)\left[x^2\left(x-3\right)-2x\left(x-3\right)-\left(x-3\right)\right]\)

\(=\left(x+1\right)\left(x-3\right)\left(x^2-2x-1\right)\)

\(=\left(x+1\right)\left(x-3\right)\left[\left(x-1\right)^2-2\right]\)

\(=\left(x+1\right)\left(x-3\right)\left(x-1-\sqrt{2}\right)\left(x-1+\sqrt{2}\right)\)

Đề bài: Phân tích đa thức thành nhân tử:

a) x^ 4- 4x^3+ 8x + 3.

b) x^2 (y^2 - 4)^2 - 6x(y^2 - 4) + 9.

c) a^4 - 9a^3 + 81a^2 - 81

phân tích đa thức thành nhân tử:

a)4a^2b^2-(a^2+b^2-1)^2

b)(xy+4)^2-(2x+2y)^2

c)x^4-2x^3-6x-9

d)x^4-2x^3+x^2-1

e)(a+1)(a^2-1)-(a-1)(a^2+1)

f)(ab-1)^2-(a-2)^2

Phân tích đa thức thành nhân tử chung

4x³y - 4xy³ - 8xy² - 4xy