因数 16x^2+2x+1/16

解

因数

16 x^{2} + 2 x + \frac{1}{16}

(4 x + \frac{1}{4})^{2}

解答ステップ

16 x^{2} + 2 x + \frac{1}{16}

a^{2} + 2 ab + b^{2}

の形式で書き直す

:

16 x^{2} = (4 x)^{2}

\frac{1}{16} = (\frac{1}{4})^{2}

2 x = 2 \cdot 4 x \frac{1}{4}

= (4 x)^{2} + 2 \cdot 4 x \frac{1}{4} + (\frac{1}{4})^{2}

完全平方式を適用する:

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

(4 x)^{2} + 2 \cdot 4 x \frac{1}{4} + (\frac{1}{4})^{2} = (4 x + \frac{1}{4})^{2}

= (4 x + \frac{1}{4})^{2}