因式分解 25x^2-10x+1-36z^2

解答

因式分解

25 x^{2} - 10 x + 1 - 36 z^{2}

(5 x - 1 + 6 z) (5 x - 1 - 6 z)

求解步骤

25 x^{2} - 10 x + 1 - 36 z^{2}

因式分解

25 x^{2} - 10 x + 1 : (5 x - 1)^{2}

= (5 x - 1)^{2} - 36 z^{2}

化简

36 z^{2} : (6 z)^{2}

= (5 x - 1)^{2} - (6 z)^{2}

使用平方差公式:

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

(5 x - 1)^{2} - (6 z)^{2} = ((5 x - 1) + 6 z) ((5 x - 1) - 6 z)

= ((5 x - 1) + 6 z) ((5 x - 1) - 6 z)

使用法则:

(a) = a

(5 x - 1) = 5 x - 1

= (5 x - 1 + 6 z) (5 x - 1 - 6 z)

f a c t or 100 x^{2} - 80 x y + 16 y^{2}

s im pl i f y (6 n^{3})^{2}

f a c t or - 4 a^{2} - 23 a - 6

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

s im pl i f y \frac{k \cdot ( \frac{27}{2} )}{( \frac{9}{4} ) i}