(a+b)³-(a-b)³=a³+3a²b+3ab²+b³-(a³-3a²b+3ab²-b³)

                    =a³+3a²b+3ab²+b³-a³+3a²b-3ab²+b³

                        =6a²b+2b³

Áp dụng hđt a³-b³=(a-b)(a²+ab+b²) ấy

\(\left(a+b\right)^3-\left(a-b\right)^3=\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

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

\(=2b\left(3a^2+b^2\right)\)

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

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

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

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

Đề sai rồi bạn phải + 2 chứ

bạn tách nhỏ câu hỏi ra

19. 3x²-4x+1

= 3x²-3x-x+1

= (3x²-3x)-(x-1)

= 3x(x-1)-(x-1)

= (3x-1)(x-1)

20.3x²+4x-7

= 3x²+3x-7x-7

= (3x²+3x)-(7x+7)

= 3x(x+1)-7(x-1)

= (3x-7)(x-1)

21.3x²+7x-6

= 3x²+9x-2x-6

= (3x²+9x)-(2x+6)

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

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

22.3x²+3x-6

= 3x²+6x-3x-6

=(3x²+6x)-(3x+6)

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

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

= 3(x-1)(x+2)

23. 3x²-3x-6

=(3x²-6x)+(3x-6)

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

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

= 3(x+1)(x-2)

24.6x²-13x+6

= 6x²-9x-4x+6

= (6x²-9x)-(4x-6)

=3x(2x-3)-2(2x-3)

=(3x-2)(2x-3)

25.6x²+13x+6

= 6x²+9x+4x+6

= (6x²+9x)+(4x+6)

=3x(2x+3)+2(2x+3)

=(3x+2)(2x+3)

26. 6x²+15x+6

= (6x²+12x)+(3x+6)

= 6x(x+2)+3(x+2)

=(6x+3)(x+2)

=3(2x+1)(x+2)

27. 6x²-15x+6

= (6x²-12x)-(3x-6)

= 6x(x-2)-3(x-2)

=(6x-3)(x-2)

=3(2x-1)(x-2)

28. 6x²+20x+6

= (6x²+18x)+(2x+6)

= 6x(x+3)+2(x+3)

= (6x+2)(x+3)

= 2(3x+1)(x+3)

29.6x²-20x+6

= (6x²-18x)-(2x-6)

= 6x(x-3)+2(x-3)

= (6x-2)(x-3)

= 2(3x-1)(x-3)

30.6x²+12x+6

= (6x²+6x)+(6x+6)

= 6x(x+1)+6(x+1)

= (6x+6)(x+1)

= 6(x+1)(x+1)

= 6(x+1)²

Bài 2 : phân tích các đa thức sau thành nhân tử

a, x3 - 2x2 + x

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

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

b, x2 - 2x - y2 + 1

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

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

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

vt mũ hộ mk đuy bạn :

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

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

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

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

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

\(b,x^2-2x-y^2+1\)

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

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

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

\(a,a^2\left(a-b\right)+ab\left(a-c\right)=a\left(a+b\right)\left(a-c\right)\\ c,=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\\ b,=\left(x-5\right)^2-9y^2=\left(x-5-3y\right)\left(x-5+3y\right)\\ d,=4\left(x^2-9x+14\right)=4\left(x-7\right)\left(x-2\right)\)

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

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

c) \(=x\left(x+3\right)+2\left(x+3\right)=\left(x+3\right)\left(x+2\right)\)

5x² + 6xy + y²

= 5x² + 5xy + xy + y²

= ( 5x² + 5xy ) + ( xy + y² )

= 5x( x + y ) + y( x + y )

= ( x + y )( 5x + y )

\(5x^2+6xy+y^2\)   

\(=5x^2+5xy+xy+y^2\)   

\(=5x\left(x+y\right)+y\left(x+y\right)\)   

\(=\left(x+y\right)\left(5x+y\right)\)

Giải thích: `x^2-5x+1`

`=x^2-2. 5/2x+25/4-21/4`

`=(x-5/2)^2-21/4`

`=(x-5/2-\sqrt{21}/2)(x-5/2+\sqrt{21}/2)`

`=(x-[5+\sqrt{21}]/2)(x-[5-\sqrt{21}]/2)`