因数 (5a-3b)^2+8(5a-3b)+16

解

因数

(5 a - 3 b)^{2} + 8 (5 a - 3 b) + 16

(5 a - 3 b + 4)^{2}

解答ステップ

(5 a - 3 b)^{2} + 8 (5 a - 3 b) + 16

(5 a - 3 b)^{2} + 8 (5 a - 3 b) + 16

を書き換え

(5 a - 3 b)^{2} + 2 (5 a - 3 b) \cdot 4 + 4^{2}

= (5 a - 3 b)^{2} + 2 (5 a - 3 b) \cdot 4 + 4^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = (5 a - 3 b), b = 4

= ((5 a - 3 b) + 4)^{2}

改良

= (5 a + 4 - 3 b)^{2}