a) (x+3)(x^2-3x+9)-(54+x^3)

= x^3- 3x^2+9x+3x^2-9x+27-54-x63

= -27

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

= (2x + y)[(2x)^2 – 2x.y + y^2] – (2x – y)[(2x)^2 + 2x.y + y^2]

= [(2x)3^3+ y^3] – [(2x)^3 – y^3]

= (2x)^3 + y^3 – (2x)^3 + y^3

= 2y^3

a)(x+3)(X^2-3x+9)-(54+x^3)

= \(x^3\)+ \(3^3 \) - 54 -\(x^3\)

= 27- 54

= -27

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

= \((2x)^3\) + \(y^3\)  - [\((2x)^3\) - \(y^3\) ]

= \(8x^3\) + \(y^3\) - \(8x^3\) + \(y^3\)

= \(2y^3\)

a) Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3+27-54-x^3\)

=-27

a: \(\left(3x+4y\right)\left(9x^2-12y+16y^2\right)\)

\(=27x^3-36xy+48xy^2+36x^2y-48y^2+64y^3\)

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

\(=x^3+9x^2+27x+27-\left(9x^2-6x+1\right)\)

\(=x^3+9x^2+27x+27-9x^2+6x-1\)

\(=x^3+33x+26\)

`#3107.101107`

`1.`

`a,`

`(3x + 4y)(9x^2 - 12xy + 16y^2)?`

`= (3x)^3 + (4y)^3`

`= 27x^3 + 64y^3`

`b,`

`(x + 3)^3 - (3x - 1)^2`

`= x^3 + 9x^2 + 27x + 27 - (9x^2 - 6x + 1)`

`= x^3 + 9x^2 + 27x + 27 - 9x^2 + 6x - 1`

`= x^3 + 33x + 26`

_____

Sử dụng HĐT:

`A^3 + B^3 = (A + B)(A^2 + AB + B^2)`

`(A + B)^3 = A^3 + 3A^2B + 3AB^2 + B^3`

`(A - B)^2 = A^2 - 2AB + B^2.`

D  nhá!!

(-3*x-1)*y+3*x^2+x

D.(x - y)(3x + 1)

\(\left(x+2y\right)^2-\left(x-2y\right)^2\\ =\left[\left(x+2y\right)-\left(x-2y\right)\right]\left[\left(x+2y\right)+\left(x-2y\right)\right]\\ =\left(x+2y-x+2y\right)\left(x+2y+x-2y\right)\\ =4y.\left(2x\right)\\ =8xy\)

\(\left(3x+y\right)^2+\left(x-y\right)^2\\ =\left[\left(3x\right)^2+2.3x.y+y^2\right]+\left(x^2-2xy+y^2\right)\\ =6x^2+6xy+y^2+x^2-2xy-y^2\\ =7x^2+4xy\)

\(-\left(x+5\right)^2-\left(x-3\right)^2\\ =-\left(x^2+10x+25\right)-\left(x^2-6x+9\right)\\ =-x^2-10x-25-x^2+6x-9\\ =-2x^2-4x-34\)

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

   b) (x+3).(x^2-3x+9)=x³+3³

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

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

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

\(=\left(2x+y\right)\left(8x^2+2y^2\right)\)

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

\(A=\left(2x+y\right)^2+\left(2x-y\right)^2+\left(4x^2-y^2\right)+3y\\ =\left(4x^2+4xy+y^2\right)+\left(4x^2-4xy+y^2\right)+\left(4x^2-y^2\right)+3y\\ =4x^2+4x^2+4x^2+4xy-4xy+y^2+y^2-y^2+3y=12x^2+3y-y^2\\ B=\left(x-2\right)\left(x+2\right)-\left(x+2\right)^2\\ =\left(x+2\right)\left(x-2-x-2\right)=-4\left(x+2\right)=-4x-8\\ C=\left(3x-4y\right)^2+\left(3x-4y\right)^2\\ =\left(9x^2-24xy+16y^2\right)+\left(9x^2-24xy+16y^2\right)\\ =18x^2-48xy+32y^2\)

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

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

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

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

\(=y^2\)