Question

factorizar :(x+1)⁴-(x-1)⁴

Answer 1

(x+1)⁴-(x-1)⁴

Usando a²-b² = (a+b)(a-b)

factorizamos

((x+1)²- (x-1)²) ×((x+1)²+ (x-1)²)

Usando :
a² - b² = (a+b)(a-b)

((x+1)²- (x-1)²)

(x+1 -(x-1) )× (x+1 +x-1)

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Usando:

(a+b)²= a² + 2ab +b²

(x+1)²

x² +2x×1 +1²

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Usando:

(a-b)² = a² -2ab -b²

(x-1)²

x² -2x×+1 +1²

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Reorganizamos los términos anteriormente calculados.

(x+1 -(x-1) )× (x+1 +x-1) ×( x² +2x×1 +1² +x² -2x×+1 +1²)


(x+1 -(x-1) )× (x+1 +x-1) ×( x² +2x +1 +x² -2x +1)


(x+1 -x-1) )× (1x +1x) ×( 1x² +2 +1x² )

(2)× (2x) × (2x² +2)

2× 2x × 2(x²+1)

4x × 2(x²+1)

8x(x²+1)