因数 (x+y)^2+8(x+y)+16

解

因数

(x + y)^{2} + 8 (x + y) + 16

(x + y + 4)^{2}

解答ステップ

(x + y)^{2} + 8 (x + y) + 16

(x + y)^{2} + 8 (x + y) + 16

を書き換え

(x + y)^{2} + 2 (x + y) \cdot 4 + 4^{2}

= (x + y)^{2} + 2 (x + y) \cdot 4 + 4^{2}

完全平方式を適用する:

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

a = (x + y), b = 4

= ((x + y) + 4)^{2}

改良

= (x + y + 4)^{2}