因数 (x+1)^2-(7x+4)^2

解

因数

(x + 1)^{2} - (7 x + 4)^{2}

- 3 (8 x + 5) (2 x + 1)

解答ステップ

(x + 1)^{2} - (7 x + 4)^{2}

2乗の差の公式を適用する:

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

(x + 1)^{2} - (7 x + 4)^{2} = ((x + 1) + (7 x + 4)) ((x + 1) - (7 x + 4))

= ((x + 1) + (7 x + 4)) ((x + 1) - (7 x + 4))

簡素化

((x + 1) + (7 x + 4)) ((x + 1) - (7 x + 4)) : (8 x + 5) (- 6 x - 3)

= (8 x + 5) (- 6 x - 3)

因数

- 6 x - 3 : - 3 (2 x + 1)

= (8 x + 5) (- 3 (2 x + 1))

規則を適用する:

a (- b) = - ab

(8 x + 5) (- 3 (2 x + 1)) = - (8 x + 5) \cdot 3 (2 x + 1)

= - (8 x + 5) \cdot 3 (2 x + 1)

= - 3 (8 x + 5) (2 x + 1)