a,\(\left(2x-1\right)\left(4x^2+2x+1\right)=\left(2x-1\right)\left[\left(2x\right)^2+2x.1+1^2\right]\)

\(=\left(2x\right)^3-1=8x^3-1\)

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

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

`a)(2x-1)(4x^2+2x+1)`

`=(2x-1)[(2x)^2+2x.1+1^2]`

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

`=8x^3-1`

Áp dụng HĐT:`A^3-B^3=(A-B)(A^2+AB+B^2)`

`b)(x+2y+z)(x+2y-z)`

`=[(x+2y)+z][(x+2y)-z]`

`=(x+2y)^2-z^2`

`=x^2+2.x.2y+(2y)^2-z^2`

`=x^2+4xy+4y^2-z^2`

Áp dụng HĐT:`A^2-B^2=(A+B)(A-B)`

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

\(a,\left(-4xy-5\right)\left(5-4xy\right)=\left(4xy+5\right)\left(4xy-5\right).\)

\(=\left(4xy\right)^2-5^2=16x^2y^2-25\)

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

\(=\left(ab^2\right)^2-\left(a^2b\right)^2=a^2b^4-a^4b^2\)

\(c,\left(3x-4\right)^2+2\left(3x-4\right)\left(4-x\right)+\left(4-x\right)^2\)

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

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

\(d,\left(a^2+ab+b^2\right)\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)

\(=\left[\left(a^2+b^2\right)+ab\right]\left[\left(a^2+b^2\right)-ab\right]-\left(a^4+b^4\right)\)

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

\(=a^4+2a^2b^2+b^4-a^2b^2-a^4-b^4=a^2b^2\)

a,\(\left(x^2+2xy\right)^3=\left(x^2\right)^3+3.\left(x^2\right)^2.2xy+3.\left(2xy\right)^2.x^2+\left(2xy\right)^3\)

\(=x^6+6x^5y+12x^4y^2+8x^3y^3\)

b,\(\left(3x^2-2y\right)^3=\left(3x^2\right)^3-3.\left(3x^2\right)^2.2y+3.\left(2y\right)^2.3x^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36y^2x^2-8y^3\)

c,\(\left(2x^3-y^2\right)^3=8x^9-12x^6y^2+6x^3y^4-y^6\)

a) Ta có: \(\left(x-3\right)^3\)

\(=x^3-3\cdot x^2\cdot3+3\cdot x\cdot3^2-3^3\)

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

b) Ta có: \(\left(2x-3\right)^3\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2-3^3\)

\(=8x^3-36x^2+54x-27\)

c) Ta có: \(\left(x-\frac{1}{2}\right)^3\)

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

\(=x^3-\frac{3}{2}x^2+\frac{3}{4}x-\frac{1}{8}\)

d) Ta có: \(\left(x^2-2\right)^3\)

\(=\left(x^2\right)^3-3\cdot\left(x^2\right)^2\cdot2+3\cdot x^2\cdot2^2-2^3\)

\(=x^6-6x^4+12x^2-8\)

e) Ta có: \(\left(2x-3y\right)^3\)

\(=\left(2x\right)^3-2\cdot\left(2x\right)^2\cdot3y+2\cdot2x\cdot\left(3y\right)^2-\left(3y\right)^3\)

\(=8x^3-24x^2y+36xy^2-27y^3\)

f) Ta có: \(\left(\frac{1}{2}x-y^2\right)^3\)

\(=\left(\frac{1}{2}x\right)^3-3\cdot\left(\frac{1}{2}x\right)^2\cdot y^2+3\cdot\frac{1}{2}x\cdot\left(y^2\right)^2-\left(y^2\right)^3\)

\(=\frac{1}{8}x^3-\frac{3}{4}x^2y^2+\frac{3}{2}xy^4-y^6\)

a,\(\left(2x^3y-0,5x^2\right)^3=\left(2x^3y\right)^3-3.\left(2x^3y\right)^2.\left(0,5x^2\right)+3.\left(0,5x^2\right)^2.\left(2x^3y\right)-\left(0,5x^2\right)^3\)

\(=8x^9y^3-6x^8y^2+\frac{3}{2}x^7y-\frac{1}{8}x^6\)

b,\(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=\left(x-3y\right)\left[x^2+x.3y+\left(3y\right)^2\right]\)

\(=x^3-\left(3y\right)^3=x^3-27y^3\)

\(\left(x^2-3\right)\left(x^4+3x^2+9\right)=\left(x^2-3\right)\left[\left(x^2\right)^2+3.x^2+3^2\right]\)

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

a, \(\left(3-x\right)^2=9-6x+x^2\)

b, \(\left(x-\frac{1}{2}\right)^2=x^2-x+\frac{1}{4}\)

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

a) \(\left(2x-1\right)\left(4x^2+2x+1\right)=8x^3-1\)

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

a) \(\left(2x-1\right)\left(4x^2+2x+1\right)=\left(2x\right)^3-1^3=8x^3-1\)

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

a) \(\left(x^2+2xy\right)^3\)

\(=\left(x^2\right)^3+3\left(x^2\right)^22xy+3x^2\left(2xy\right)^2+\left(2xy\right)^3\)

\(=x^6+6x^5y+12x^4y^2+8x^3y^3\)

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

\(=\left(3x^2\right)^3-3\left(3x^2\right)^22y+3.3x^2\left(2y\right)^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3\)

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

\(=\left(2x^3\right)^3-3\left(2x^3\right)^2y^2+3.2x^3\left(y^2\right)^2-\left(y^2\right)^3\)

\(=8x^9-12x^6y^2+6x^3y^4-y^6.\)

a) \(\left(2x^3y-0,5x^2\right)^3\)

\(=\left(2x^3y\right)^3-3\left(2x^3y\right)^20,5x^2+3.2x^3y\left(0,5x^2\right)^2-\left(0,5x^2\right)^3\)

\(=8x^9y^3-6x^8y^2+1,5x^7y-0,125x^6\)

b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

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

\(=x^3-27y^3\)

c) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)

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

\(=x^3-27.\)