Bài 8: Phân tích đa thức thành nhân tử bằng phương pháp nhóm các hạng tử

=(x-5)(x-8)(x-6)(x-7)-9

=(x^2-13x+40)(x^2-13x+42)-9

=(x^2-13x)^2+82(x^2-13x)+40*42-9

=(x^2-13x)^2+82(x^2-13x)+1671

\(=\left(x^2-13x\right)^2+82\left(x^2-13x\right)+1681-10\)

\(=\left(x^2-13x+41\right)^2-10\)

\(=\left(x^2-13x+41-\sqrt{10}\right)\left(x^2-13x+41+\sqrt{10}\right)\)

\(a.x^3-2x^2-2x-4\\ =\left(x^3-2x^2\right)-\left(2x-4\right)\\ =x^2\left(x-2\right)-2\left(x-2\right)\\ =\left(x^2-2\right)\left(x-2\right)\)

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

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

\(d.16-x^2+2xy-y^2\\ =4^2-\left(x-y\right)^2\\ =\left(4-x+y\right)\left(4-x-y\right)\)

b: =xy-x-y+1

=x(y-1)-(y-1)

=(x-1)(y-1)

c: =(x-2y)^2-4y

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

d: =16-(x^2-2xy+y^2)

=16-(x-y)^2

=(4-x+y)(4+x-y)

`10x(x-y) - 8y(y-x)`

`= 10x(x-y) + 8y(x-y)`

`= (10x+8y)(x-y)`

`= 2(5x+4y)(x-y)`

\(10x\left(x-y\right)-8y\left(y-x\right)\)

\(=10x\cdot\left(x-y\right)-8y\cdot-\left(x-y\right)\)

\(=10x\left(x-y\right)+8y\left(x-y\right)\)

\(=\left(10x+8y\right)\left(x-y\right)\)

\(=\left(2\cdot5x+2\cdot4y\right)\left(x-y\right)\)

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

64x^4+y^4

=64x^4+16x^2y^2+y^4-16x^2y^2

=(8x^2+y^2)^2-(4xy)^2

=(8x^2-4xy+y^2)(8x^2+4xy+y^2)

a: \(=-x^2y\cdot x+x^2y\cdot y=x^2y\left(-x+y\right)\)

b: \(=-xy^2\cdot x^2-xy^2\cdot z=-xy^2\left(x^2+z\right)\)

c: x^2y^3-xy^2

=xy^2*xy-xy^2

=xy^2(xy-1)

d: -x^3z-z

=z(-x^3-1)

=-z(x+1)(x^2-x+1)

e: =x(x-y)+(x-y)

=(x-y)(x+1)

n: =x^2(x-1)-(x-1)

=(x-1)(x^2-1)

=(x-1)^2(x+1)

phân tích đa thức thành nhân tử

\(a,\)

\(x^3y-y\)

\(=y\left(x^3-1\right)\)

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

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

\(b,\)

\(x^3y+y\)

\(=y\left(x^3+1\right)\)

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

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

\(c,\)

\(\left(x-y\right)^2-x\left(y-x\right)\)

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

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

\(=\left(x-y\right)\left(2x-y\right)\)

=x^8+2x^4+1-100x^4

=(x^4+1)^2-100x^4

=(x^4-10x^2+1)(x^4+10x^2+1)

=x^8+2x^4+1+96x^4

=(x^4+1)^2+96x^4

=(x^4+8x^2+1)^2-16x^2(x^2-1)^2

=(x^4+4x^3+8x^2-4x+1)(x^4-4x^3+8x^2+4x+1)

  đây ạ

14: =x^3-3x^2+3x-1-1

=(x-1)^3-1

=(x-1-1)(x^2-2x+1+x-1+1)

=(x-2)(x^2-x+1)

15: =x^3+x^2-4x^2-4x+7x+7

=(x+1)(x^2-4x+7)

16: =2x^3-x^2-2x^2+x+2x-1

=(2x-1)(x^2-x+1)

5

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

6

\(=4^2-\left(3x+1\right)^2=\left(4-3x-1\right)\left(4+3x+1\right)=\left(3-3x\right)\left(5+3x\right)\\ =3\left(1-x\right)\left(5+3x\right)\)

7

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

8

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

9

\(=\left(2x\right)^2-2.2x.y+y^2=\left(2x-y\right)^2\)

10

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

11

\(=\left(x^2y^2\right)^2+2.2x^2y^2+2^2=\left(x^2y^2+2\right)\)

12

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

13

\(=1-\left(3\sqrt{3}x\right)^3=\left(1-3\sqrt{3}x\right)\left[1^2+3\sqrt{3}.x+\left(3\sqrt{3}.x\right)^2\right]=\left(1-3\sqrt{3}x\right)\left(1+3\sqrt{3}x+27x^2\right)\)

  đây