因式分解 4y^4-5y^2+1

解答

因式分解

4 y^{4} - 5 y^{2} + 1

(2 y + 1) (2 y - 1) (y + 1) (y - 1)

求解步骤

4 y^{4} - 5 y^{2} + 1

令

u = y^{2}

= 4 u^{2} - 5 u + 1

因式分解

4 u^{2} - 5 u + 1 : (4 u - 1) (u - 1)

= (4 u - 1) (u - 1)

u = y^{2}

代回

= (4 y^{2} - 1) (y^{2} - 1)

因式分解

4 y^{2} - 1 : (2 y + 1) (2 y - 1)

= (2 y + 1) (2 y - 1) (y^{2} - 1)

因式分解

y^{2} - 1 : (y + 1) (y - 1)

= (2 y + 1) (2 y - 1) (y + 1) (y - 1)

s im pl i f y 6 x - 2 y + 7 - (2 x + 3)

s im pl i f y (7 \cdot x^{3 n - 2} - 5) (7 \cdot x^{3 n - 2} + 9)

f a c t or 4 x^{2} - 9 y^{2} + 20 x + 25

s im pl i f y \frac{3}{( x ^{2} - 4 )} + \frac{1}{( x - 2 ) ^{2}}

f a c t or a^{10} + x^{10}