a) Ta có: \(a^3y^3+125\)

\(=\left(ay+5\right)\left(a^2y^2-5ay+25\right)\)

b) Ta có: \(8x^3-y^3-6xy\cdot\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)-6xy\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x^2+2xy-6xy+y^2\right)\)

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

16x^4_y2-25a²b²

1) \(x^6+1\)

\(=x^6+x^4-x^4+x^2-x^2+1\)

\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)

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

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

2) \(x^6-y^6\)

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

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

3) \(5x^2y^4-10x^4y^2+5x^2y^2\)

\(=5x^2y^2\left(y^2-2x^2+1\right)\)

4) \(25a^2-49b^2\)

\(=\left(5a+7b\right)\left(5a-7b\right)\)

5) \(36\left(x-y\right)^2-25\left(2x-1\right)^2\)

\(=\left[6\left(x-y\right)+5\left(2x-1\right)\right]\left[6\left(x-y\right)-5\left(2x-1\right)\right]\)

\(=\left[6x-6y+10x-5\right]\left[6x-6y-10x+5\right]\)

\(=\left(16x-6y-5\right)\left(-4x-6y+5\right)\)

b)  \(64x^3+1=\left(4x+1\right)\left(16x^2-4x+1\right)\)\

c) \(x^3y^6z^9-125=\left(xy^2z^3-5\right)\left(x^2y^4z^6+5xy^2z+25\right)\)

d)  \(27x^6-8x^3=x^3\left(27x^3-8\right)=x^3\left(3x-2\right)\left(9x^2+6x+4\right)\)

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

64x³ + 1

= ( 4x )³  +  1

= ( 4x + 1 ) ( 16x² - 4x + 1 )

Hằng đẳng thức 6 : A³ + B³

27x⁶ - 8x³

= ( 3x²)³ + ( 2x )³

= ( 3x + 2x ) ( 9x² - 6x + 4x² )

HĐT 6

x⁶ - y⁶

= ( x² )³ - ( y² )³

= ( x² - y² ) ( x⁴ + x²y² + y⁴ )

HĐT 7 : A³ - B³

x³y⁶z⁹ + 1

= ( xy²z³)³ + 1

= ( xy²z³ + 1 ) ( x²y⁴z⁶ + zy²z³ + 1 )

HĐT 6

Ta có : x⁶ - x⁶ 

= ( x²)³  - ( y²)³ 

= ( x² - y² ) ( x⁴ + x²y² + y⁴ ) 

= (x - y)(x + y) ( x⁴ + x²y² + y⁴ ) 

b, <=>(4x)³+1³ 

<=> (4x+1)( 16x²-4x+1)

c, <=> (x.y².z³)³-5³

<=> (xy²z³-5)( x²y⁴z⁶+5xy²z³+25)

d, <=> (3x²)³-(2x)³

<=> (3x²-2x)(9x⁴+6x³+4x²)

d, (x³)²- (y³)² 

= (x³+y³)(x³-y³)

a) \(\left(2x+5\right)^2\)\(-\left(x-9\right)^2\)

=\(\left(2x+5+x-9\right).\left(2x+5-x+9\right)\)

=\(\left(3x-4\right).\left(x+14\right)\)

bài 1: a) \(x^2-3=x^2-\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)\)

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

c) \(x^3-27b^3=\left(x-3b\right)\left(x^2+3xb+b^2\right)\)