What is factor x^4-(x-2)^4 ?

The solution to factor x^4-(x-2)^4 is 8(x^2-2x+2)(x-1)

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factor x^4-(x-2)^4

factor

x^{4} - (x - 2)^{4}

8 (x^{2} - 2 x + 2) (x - 1)

Solution steps

x^{4} - (x - 2)^{4}

x^{4} = (x^{2})^{2}

(x - 2)^{4} = ((x - 2)^{2})^{2}

= (x^{2})^{2} - ((x - 2)^{2})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2})^{2} - ((x - 2)^{2})^{2} = (x^{2} + (x - 2)^{2}) (x^{2} - (x - 2)^{2})

= (x^{2} + (x - 2)^{2}) (x^{2} - (x - 2)^{2})

Factor

x^{2} - (x - 2)^{2} : 4 (x - 1)

= (x^{2} + (x - 2)^{2}) \cdot 4 (x - 1)

Expand

x^{2} + (x - 2)^{2} : 2 x^{2} - 4 x + 4

= (2 x^{2} - 4 x + 4) \cdot 4 (x - 1)

= 4 (2 x^{2} - 4 x + 4) (x - 1)

Factor

2 x^{2} - 4 x + 4 : 2 (x^{2} - 2 x + 2)

= 4 \cdot 2 (x^{2} - 2 x + 2) (x - 1)

Multiply the numbers:

4 \cdot 2 = 8

= 8 (x^{2} - 2 x + 2) (x - 1)

0 = - \frac{3}{2} x + 3

128 = x^{2}

3 x = - 27

2 x = - 8

\frac{8}{6} - \frac{1}{8}

What is factor x^4-(x-2)^4 ?
The solution to factor x^4-(x-2)^4 is 8(x^2-2x+2)(x-1)