Question

*Fatore:
a) 3x^4 - 12x^8
b)3x^2 - 75
c)a^2 - x^2 +a +x
d)2x^2 -12x +18
e)a^5b -a^3b^3 +a^4b^2-a^2^4

Answer 1

a
3x⁴ - 12x⁸
3x⁴ ( 1 - 4x⁴ ) = 3x⁴ ( 1 + 2x²) ( 1 - 2x² )
b
3x² - 75 = 3( x² - 25) = 3 ( ( x + 5)(x - 5)
C
a² - x² + (a + x ) = ( a + x)(a-x) + ( a + x)  =
d
2x² - 12x + 18 = 0
x² - 6x + 9 = 0
( x - 3)² =
e
a⁽⁵ᵇ⁾ - a⁽³ᵇ³⁾ + a⁽⁴ᵇ²⁾- (a² )⁴ =
(a⁽⁵ᵇ⁾- a⁽³ᵇ³⁾)+ (a⁽⁴ᵇ²⁾ - a⁽⁸⁾)=
a⁽³ᵇ⁾ ( a² - b²) + a⁴( a(ᵇ²) - a⁴ ) = 
a³ᵇ ( a + b)( a - b) + a⁴ ( aᵇ + a² ) (aᵇ - a²) =
(a³ᵇ + a⁴ ) ( a + b)(a-b) ( aᵇ + a²) ( aᵇ - a²)