因数 9u^2+24uv+16v^2

解

因数

9 u^{2} + 24 uv + 16 v^{2}

(3 u + 4 v)^{2}

解答ステップ

9 u^{2} + 24 uv + 16 v^{2}

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

の形式で書き直す

:

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

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

24 uv = 2 \cdot 3 u \cdot 4 v

= (3 u)^{2} + 2 \cdot 3 u \cdot 4 v + (4 v)^{2}

完全平方式を適用する:

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

(3 u)^{2} + 2 \cdot 3 u \cdot 4 v + (4 v)^{2} = (3 u + 4 v)^{2}

= (3 u + 4 v)^{2}