a) Rút gọn được A = ( k 3  – 64) – (128 +  k 3 ) = -192.

b) Rút gọn được B = -19 m 3  + 35 n 3 .

Bài 1: 

a: Ta có: \(A=\left(k-4\right)\left(k^2+4k+16\right)-\left(k^3+128\right)\)

\(=k^3-64-k^3-128\)

=-192

b: Ta có: \(B=\left(2m+3n\right)\left(4m^2-6mn+9n^2\right)-\left(3m-2n\right)\left(9m^2+6mn+4n^2\right)\)

\(=8m^3+27n^3-27m^3+8n^3\)

\(=-19m^3+35n^3\)

Bài 4: 

a: Ta có: \(\left(x-1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=16\)

\(\Leftrightarrow x^3-3x^2+3x-1+8-x^3+3x^2+6x=16\)

\(\Leftrightarrow9x=9\)

hay x=1

b: ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)

\(\Leftrightarrow x^3+8-x^3+2x=15\)

\(\Leftrightarrow2x=7\)

hay \(x=\dfrac{7}{2}\)

\(\left(7+2b\right)\left(4b^2-4b+49\right)\)

\(=28b^2-28b+343+8b^3-8b^2+98b\)

\(=8b^3+20b^2+70b+343\)

a) \(\left(4n^2-6nm+9m^2\right)\left(2n+3m\right)\)

\(=\left(2n+3m\right)\left[\left(2n\right)^2-2n.3m+\left(3m\right)^2\right]\)

\(=\left(2n\right)^3+\left(3m\right)^3\)

\(=8n^3+27m^3\)

b) Sửa đề \(\left(7+2b\right)\left(4b^2-14b+49\right)\)

\(=\left(7+2b\right)\left[\left(2b\right)^2-2b.7+7^2\right]\)

\(=7^3+\left(2b\right)^3\)

\(=343+8b^3\)

c) \(\left(25a^2+10ab+4b^2\right)\left(5a-2b\right)\)

\(=\left(5a-2b\right)\left[\left(5a\right)^2+5a.2b+\left(2b\right)^2\right]\)

\(=\left(5a\right)^3-\left(2b\right)^3\)

\(=125a^3-8b^3\)

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

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

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

a ) \(\left(a^6-3a^3+9\right)\left(a^3+3\right)=a^9+27\)

b ) Đặt \(a-y=t\) , ta có :

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

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

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

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

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

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

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

c ) \(\left(4n^2-6mn+9m^2\right)\left(2n+3m\right)=8n^3+27m^3\)

d ) \(\left(25a^2+10ab+4b^2\right)\left(5a-2b\right)=125a^3-8b^3\)

a, ( a⁶ - 3a³ + 9 )(a³+ 3) = (a³)³ - 3³ = a⁹ - 27

b, ( a-x-y)³ - (a+x-y)³ = (a-x-y-a+x-y)(a-x-y+a+x-y)

= (-2y)(2a-2y) = -2y.2(a-y)

c, (4n²- 6mn + 9m²)(2n + 3m) = (2n)³ + (3m)³

= 8n³ + 27m³

d, (25a² + 10ab +4b²)( 5a - 2b ) = 125a³ - 8b³

1: 2a+2b=2(a+b)

2: 2a+4b+6c

=2*a+2*2b+2*3c

=2(a+2b+3c)

3: \(-7a-14ab-21b=-7\left(a+2ab+3b\right)\)

4: \(2ax-2ay+2a=2a\left(x-y+1\right)\)

5: \(=3a\cdot ax-3a\cdot2ay+3a\cdot4=3a\left(ax-2ay+4\right)\)

6: \(=2\cdot2ax-2\cdot ay-2\cdot1=2\cdot\left(2ax-ay-1\right)\)

7: =a^2-(2b)^2

=(a-2b)(a+2b)

8: =(5a)^2-1^2

=(5a-1)(5a+1)

9: =9(16a^2-9)

=9(4a-3)(4a+3)

a: m>n

=>2m>2n

=>2m-2>2n-2

b: m>n

=>-3m<-3n

=>-3m+1<-3n+1

c: m>n

=>2m>2n

=>2m+3>2n+3

mà 2n+3>2n+1

nên 2m+3>2n+1

d: m>n

=>-5m<-5n

=>-5m+3<-5n+3

mà -5n+3<-5n+7

nên -5m+3<-5n+7