因数 4h^2-12hk+9k^2

解

因数

4 h^{2} - 12 hk + 9 k^{2}

(2 h - 3 k)^{2}

解答ステップ

4 h^{2} - 12 hk + 9 k^{2}

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

の形式で書き直す

:

4 h^{2} = (2 h)^{2}

9 k^{2} = (3 k)^{2}

- 12 hk = - 2 \cdot 2 h \cdot 3 k

= (2 h)^{2} - 2 \cdot 2 h \cdot 3 k + (3 k)^{2}

完全平方式を適用する:

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

(2 h)^{2} - 2 \cdot 2 h \cdot 3 k + (3 k)^{2} = (2 h - 3 k)^{2}

= (2 h - 3 k)^{2}