a: \(\left(a-2b\right)^2-4b^2\)

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

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

=a(a-4b)

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

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

d: \(\left(a+3b\right)^2-9b^2\)

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

=(a+3b-3b)(a+3b+3b)=a(a+6b)

e: \(\left(x-3\right)^3-27\)

\(=\left(x-3-3\right)\left\lbrack\left(x-3\right)^2+3\left(x-3\right)+9\right\rbrack\)

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

f: \(\left(x+1\right)^3-125\)

\(=\left(x+1-5\right)\left\lbrack\left(x+1\right)^2+5\left(x+1\right)+25\right\rbrack\)

\(=\left(x-4\right)\left(x^2+2x+1+5x+5+25\right)=\left(x-4\right)\left(x^2+7x+31\right)\)

dấu ^ là mũ nha mn

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

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

\(=-2x.\left[a^2+x^2+y^2-2ax+2xy-2ay+\left(a-y\right)^2-x^2+a^2+x^2+y^2+2ax-2xy-2ay\right]\)

\(=-2x\left[a^2+x^2+y^2-2ax+2xy-2ay+a^2-2ay+y^2-x^2+a^2+x^2+y^2+2ax-2xy-2ay\right]\)

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

a) x⁶ + 1 

= (x²)³ + 1³

=(x² +1)(x⁴ - x² + 1)

b) x⁶ - y⁶

= (x²)³ - (y²)³

=(x² -y²)(x⁴ + x²y² + y⁴)

= (x-y)(x+y)[ x⁴ + 2.x²y² + y⁴ - x²y² ]

=(x-y)(x+y) [(x² +y²)² - (xy)² ]

=(x-y)(x+y)(x² - xy + y²)(x² + xy + y²)

c) x⁹ +1

= (x³)³ + 1³

=(x³ +1)(x⁶ - x³ -1)

= (x+1)(x² - x +1)(x⁶ - x³-1) 

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) \(x^6-y^6\)

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

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

x⁴ - 1 = (x² - 1)(x² + 1)  =  (x - 1)(x + 1)(x² + 1)

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

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