展開する (a+d)(b+c)(d+c)(a+b)

解

展開する

(a + d) (b + c) (d + c) (a + b)

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

解答ステップ

(a + d) (b + c) (d + c) (a + b)

FOIL方法

(a + d) (b + c)

を適用します:

ab + a c + d b + d c

= (ab + a c + d b + d c) (d + c) (a + b)

FOIL方法

(d + c) (a + b)

を適用します:

a d + d b + a c + b c

= (ab + a c + d b + d c) (a d + d b + a c + b c)

括弧を分配する

= aba d + ab d b + aba c + abb c + a c a d + a c d b + a c a c + a c b c + d ba d + d b d b + d ba c + d bb c + d c a d + d c d b + d c a c + d c b c

簡素化

aba d + ab d b + aba c + abb c + a c a d + a c d b + a c a c + a c b c + d ba d + d b d b + d ba c + d bb c + d c a d + d c d b + d c a c + d c b c : a^{2} c^{2} + d^{2} b^{2} + a^{2} d b + a d b^{2} + a^{2} b c + a b^{2} c + a^{2} d c + ab c^{2} + a d^{2} b + d b^{2} c + a d^{2} c + d^{2} b c + a d c^{2} + d b c^{2} + 2 a d b c

= a^{2} c^{2} + d^{2} b^{2} + a^{2} d b + a d b^{2} + a^{2} b c + a b^{2} c + a^{2} d c + ab c^{2} + a d^{2} b + d b^{2} c + a d^{2} c + d^{2} b c + a d c^{2} + d b c^{2} + 2 a d b c