What is factor 1-50x^2+625x^4 ?

The solution to factor 1-50x^2+625x^4 is (5x+1)^2(5x-1)^2

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factor 1-50x^2+625x^4

factor

1 - 50 x^{2} + 625 x^{4}

(5 x + 1)^{2} (5 x - 1)^{2}

Solution steps

1 - 50 x^{2} + 625 x^{4}

Write in the standard form

= 625 x^{4} - 50 x^{2} + 1

Let

u = x^{2}

= 625 u^{2} - 50 u + 1

Factor

625 u^{2} - 50 u + 1 : (25 u - 1)^{2}

= (25 u - 1)^{2}

Substitute back

u = x^{2}

= (25 x^{2} - 1)^{2}

Factor

25 x^{2} - 1 : (5 x + 1) (5 x - 1)

= ((5 x + 1) (5 x - 1))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

((5 x + 1) (5 x - 1))^{2} = (5 x + 1)^{2} (5 x - 1)^{2}

= (5 x + 1)^{2} (5 x - 1)^{2}

(x^{2} - 4 x) (x^{2} - 4 x - 1) - 20

\frac{\frac{1}{5}}{cos ( x )}

(a + a)^{2}

(8) \cdot v^{2} + 4 3 v - 15

\frac{1}{( ( 5 ^{2} \cdot a ^{- 6} ) ^{- 2} )}

What is factor 1-50x^2+625x^4 ?
The solution to factor 1-50x^2+625x^4 is (5x+1)^2(5x-1)^2