What is factor x^6-15625 ?

The solution to factor x^6-15625 is (x+5)(x-5)(x^2+5x+25)(x^2-5x+25)

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factor x^6-15625

factor

x^{6} - 15625

(x + 5) (x - 5) (x^{2} + 5 x + 25) (x^{2} - 5 x + 25)

Solution steps

x^{6} - 15625

Apply exponent rules

= (x^{2})^{3} - 2 5^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x^{2})^{3} - 2 5^{3} = (x^{2} - 25) (x^{4} + 25 x^{2} + 2 5^{2})

= (x^{2} - 25) (x^{4} + 25 x^{2} + 2 5^{2})

Factor

x^{2} - 25 : (x + 5) (x - 5)

= (x + 5) (x - 5) (x^{4} + 25 x^{2} + 2 5^{2})

Factor

x^{4} + 25 x^{2} + 2 5^{2} : (x^{2} + 25 + 5 x) (x^{2} + 25 - 5 x)

= (x + 5) (x - 5) (x^{2} + 25 + 5 x) (x^{2} + 25 - 5 x)

= (x + 5) (x - 5) (x^{2} + 5 x + 25) (x^{2} - 5 x + 25)

(b^{x + 1} - 3) (b^{x + 1} - 1)

n + 1 + (- 2) n

∣ f (x) ∣^{2} - ∣ g (x) ∣^{2}

(\frac{( n - 1 )}{n})^{n}

6 x^{2} \cdot y - 4 x \cdot y^{2} + 10 x y

What is factor x^6-15625 ?
The solution to factor x^6-15625 is (x+5)(x-5)(x^2+5x+25)(x^2-5x+25)