\(P=a^{16}+a^8b^8+b^{16}=\left(a^8\right)^2+2a^8b^8+\left(b^8\right)^2-a^8b^8\)

     \(=\left(a^8+b^8\right)^2-\left(a^4b^4\right)^2\)

       \(=\left(a^8+b^8+a^4b^4\right)\left(a^8+b^8-a^4b^4\right)\)

         \(=\left(a^4+b^4+a^2b^2\right)\left(a^4+b^4-a^2b^2\right)\left(a^8+b^8-a^4b^4\right)\)

           \(=\left(a^2+b^2+ab\right)\left(a^2+b^2-ab\right)\left(a^8+b^8-a^4b^4\right)\left(a^4+b^4-a^2b^2\right)\)

a/ \(\left(x+3y\right)\left(2x-y\right)\)

b/ \(\left(x^2+2\right)\left(x^2-2\right)\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

b/ \(x^8-16=\left(x^4+4\right)\left(x^4-4\right)\)

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

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

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

\(=\left(4-a+b\right)\left(4+a-b\right)\)

x 16 + x 8 − 2 = ( x 8 ) 2 + x 8 − 2 = ( x 8 − 1 ) ( x 8 + 2 ) = ( x 4 − 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x 2 − 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x − 1 ) ( x + 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 )

a) x2 + xy –x – y = x(x + y) – (x + y) = (x + y)(x -1 ).

b) a2 – b2 + 8a + 16 = (a2 + 8a + 16) – b2 = (a + 4)2 – b2

= (a + 4 – b)(a + 4 + b).

a² - b² + 8a + 16

= ( - (b -  a - 4))(b + a + 4) 

x^8+7x^4+16=x⁸+8x⁴+16-x⁴

=(x⁴+4)²-x⁴

=(x⁴-x²+4)(x⁴+x²+4)

a)

\(2x^2y-8xy^2\\ =2xy\left(x-4y\right)\)

b)

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

Đặt đúng môn học Toán bạn nhé. -

a) x² - 9

= x² - 3²

= (x - 3)(x + 3)

b) 4x² - 1

= (2x)² - 1²

= (2x - 1)(2x + 1)

c) x⁴ - 16

= (x²)² - 4²

= (x² - 4)(x² + 4)

= (x² - 2²)(x² + 4)

= (x - 2)(x + 2)(x + 4)

d) x² - 4x + 4

= x² - 2.x.2 + 2²

= (x - 2)²

e) x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 4)

f) x³ + 3x² + 3x + 1

= x³ + 3.x².1 + 3.x.1² + 1³

= (x + 1)³