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28 tháng 6 2019

\(x^2-y^2\)

\(=x^2+xy-xy-y^2\)

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

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

28 tháng 6 2019

x²-y²=(x+y)(x-y)

25 tháng 5 2023

x⁸ + x⁴ + 1

= x⁸ + 2x⁴ + 1 - x⁴

= (x⁴ + 1)² - x⁴

= (x⁴ + 1)² - (x²)²

= (x⁴ + 1 + x²)(x⁴ + 1 - x²)

= (x⁴ + x² + 1)(x⁴ - x² + 1)

19) Ta có: \(-x^2-4x-4\)

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

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

20) Ta có: \(-4x^2-12x-9\)

\(=-\left(4x^2+12x+9\right)\)

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

21) Ta có: \(-4x^2-4x-1\)

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

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

22) Ta có: \(-x^2+6x-9\)

\(=-\left(x^2-6x+9\right)\)

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

23) Ta có: \(-x^2+10x-25\)

\(=-\left(x^2-10x+25\right)\)

\(=-\left(x-5\right)^2\)

24) Ta có: \(-x^2+8x-16\)

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

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

25) Ta có: \(-4x^2+12x-9\)

\(=-\left(4x^2-12x+9\right)\)

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

26) Ta có: \(a^2-a+b-b^2\)

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

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

13) Ta có: \(y^2-2xy+2x-y\)

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

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

14) Ta có: \(x-2xy+4y-2\)

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

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

15) Ta có: \(x^2-2xy+x-2y\)

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

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

16) Ta có: \(xy-z-y+xz\)

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

\(=\left(y+z\right)\left(x-1\right)\)

17) Ta có: \(2xy+3z-6y-xz\)

\(=\left(2xy-xz\right)+\left(3z-6y\right)\)

\(=x\left(2y-z\right)-3\left(2y-z\right)\)

\(=\left(2y-z\right)\left(x-3\right)\)

18) Ta có: \(2xy-2z+4y-xz\)

\(=\left(2xy+4y\right)+\left(xz+2z\right)\)

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

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

26) Ta có: \(x^4-20x^2+64\)

\(=x^4-16x^2-4x^2+64\)

\(=x^2\left(x^2-16\right)-4\left(x^2-16\right)\)

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

27) Ta có: \(4x^3+6x^2+3x+1\)

\(=4x^3+4x^2+2x^2+2x+x+1\)

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

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

28) Ta có: \(x^3-6x^2+12x-9\)

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

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

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

29: Ta có: \(x^4+x^2+1\)

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

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

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

9 tháng 8 2021

26) Ta có: x4−20x2+64x4−20x2+64

=x4−16x2−4x2+64=x4−16x2−4x2+64

=x2(x2−16)−4(x2−16)=x2(x2−16)−4(x2−16)

=(x−4)(x+4)(x−2)(x+2)=(x−4)(x+4)(x−2)(x+2)

27) Ta có: 4x3+6x2+3x+14x3+6x2+3x+1

=4x3+4x2+2x2+2x+x+1=4x3+4x2+2x2+2x+x+1

=4x2(x+1)+2x(x+1)+(x+1)=4x2(x+1)+2x(x+1)+(x+1)

=(x+1)(4x2+2x+1)=(x+1)(4x2+2x+1)

28) Ta có: x3−6x2+12x−9x3−6x2+12x−9

=x3−3x2−3x2+9x+3x−9=x3−3x2−3x2+9x+3x−9

=x2⋅(x−3)−3x(x−3)+3(x−3)=x2⋅(x−3)−3x(x−3)+3(x−3)

=(x−3)(x2−3x+3)=(x−3)(x2−3x+3)

29: Ta có: x4+x2+1x4+x2+1

=x4+2x2+1−x2=x4+2x2+1−x2

=(x2+1)2−x2=(x2+1)2−x2

=(x2−x+1)(x2+x+1)

=(x-y-2y)[(x-y)^2+2y(x-y)+4y^2]

=(x-3y)(x^2-2xy+y^2+2xy-2y^2+4y^2)

=(x-3y)(x^2+3y^2)

24 tháng 8 2023

\(\left(x-y\right)^3-8y^3\)

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

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

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

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

6 tháng 9 2023

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

`HaNa☘D`

 

6 tháng 9 2023

\(\left(a-b\right)^2-\left(b-a\right)\)

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

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

24 tháng 8 2023

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

24 tháng 8 2023

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

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

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

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

24 tháng 8 2023

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

24 tháng 8 2023

Các chổ này chị dùng ngoặc vuông nha 

25 tháng 8 2023

\(3x\cdot\left(x-y\right)^2-6\cdot\left(y-x\right)\)

\(=3x\left(x-y\right)^2+6\left(x-y\right)\)

\(=\left(x-y\right)\left[3x\left(x-y\right)+6\right]\)

\(=\left(x-y\right)\left(3x^2-3xy+6\right)\)

25 tháng 8 2023

(x - y)(3x2 - 3xy + 6)

17 tháng 7 2019

(x^3-3x-3)(x^6+3x^4-6x^3+9x^2-9x+9)