因数 16-(2a+b)^2

解

因数

16 - (2 a + b)^{2}

(4 + 2 a + b) (4 - 2 a - b)

解答ステップ

16 - (2 a + b)^{2}

数を因数に分解する:

16 = 4^{2}

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

2乗の差の公式を適用する:

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

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

= (4 + (2 a + b)) (4 - (2 a + b))

簡素化

(4 + (2 a + b)) (4 - (2 a + b)) : (4 + 2 a + b) (4 - 2 a - b)

= (4 + 2 a + b) (4 - 2 a - b)