因数 3rs-5cr-15cs+25c^2

解

因数

3 rs - 5 cr - 15 cs + 25 c^{2}

(r - 5 c) (3 s - 5 c)

解答ステップ

3 rs - 5 cr - 15 cs + 25 c^{2}

書き換え

= 3 sr - 5 cr - 5 \cdot 3 sc + 25 c^{2}

共通項をくくり出す

3 s

= 3 s (r - 5 c) - 5 cr + 25 c^{2}

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

c^{2} = cc

= 3 s (r - 5 c) - 5 cr + 25 cc

書き換え

= 3 s (r - 5 c) - 5 cr + 5 \cdot 5 cc

共通項をくくり出す

5 c

= 3 s (r - 5 c) + 5 c (- r + 5 c)

書き換え

= 3 (r - 5 c) s - 5 (r - 5 c) c

共通項をくくり出す

(r - 5 c)

= (r - 5 c) (3 s - 5 c)