因式分解 a^2-4b^2-10a+25

解答

因式分解

a^{2} - 4 b^{2} - 10 a + 25

(a - 5 + 2 b) (a - 5 - 2 b)

求解步骤

a^{2} - 4 b^{2} - 10 a + 25

因式分解

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

= (a - 5)^{2} - 4 b^{2}

化简

4 b^{2} : (2 b)^{2}

= (a - 5)^{2} - (2 b)^{2}

使用平方差公式:

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

(a - 5)^{2} - (2 b)^{2} = ((a - 5) + 2 b) ((a - 5) - 2 b)

= ((a - 5) + 2 b) ((a - 5) - 2 b)

使用法则:

(a) = a

(a - 5) = a - 5

= (a - 5 + 2 b) (a - 5 - 2 b)

e x p an d (7 x) (2 x + 3 y)

s im pl i f y 5 a - 3 a - 7 - 2 - 7 a + a - a

s im pl i f y \frac{( 15 x ^{3} \cdot y ^{4} )}{( 25 x y )}

s im pl i f y 5 x (a^{2} + 1) + (x + 1) (a^{2} + 1)

s im pl i f y x^{2} + 2 2 x - 5