展開する (a+b+c)m^2+(a+b+c)n^2+(a+b+c)p^2

解

展開する

(a + b + c) m^{2} + (a + b + c) n^{2} + (a + b + c) p^{2}

a m^{2} + m^{2} b + m^{2} c + a n^{2} + b n^{2} + n^{2} c + a p^{2} + b p^{2} + c p^{2}

解答ステップ

(a + b + c) m^{2} + (a + b + c) n^{2} + (a + b + c) p^{2}

= m^{2} (a + b + c) + n^{2} (a + b + c) + p^{2} (a + b + c)

拡張

m^{2} (a + b + c) : a m^{2} + m^{2} b + m^{2} c

= a m^{2} + m^{2} b + m^{2} c + n^{2} (a + b + c) + p^{2} (a + b + c)

拡張

n^{2} (a + b + c) : a n^{2} + b n^{2} + n^{2} c

= a m^{2} + m^{2} b + m^{2} c + a n^{2} + b n^{2} + n^{2} c + p^{2} (a + b + c)

拡張

p^{2} (a + b + c) : a p^{2} + b p^{2} + c p^{2}

= a m^{2} + m^{2} b + m^{2} c + a n^{2} + b n^{2} + n^{2} c + a p^{2} + b p^{2} + c p^{2}