Question
Simplify the expression
a3−b3−c3−3a2b−3a2c+3b2a−3b2c+3c2a−3c2b+6abc
Evaluate
(a−b−c)3
Use (a+b+c)3=a3+b3+c3+3a2b+3a2c+3b2a+3b2c+3c2a+3c2b+6abc to expand the expression
a3+(−b)3+(−c)3+3a2(−b)+3a2(−c)+3(−b)2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
a3−b3+(−c)3+3a2(−b)+3a2(−c)+3(−b)2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
a3−b3−c3+3a2(−b)+3a2(−c)+3(−b)2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Multiply the numbers
a3−b3−c3−3a2b+3a2(−c)+3(−b)2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Multiply the numbers
a3−b3−c3−3a2b−3a2c+3(−b)2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
a3−b3−c3−3a2b−3a2c+3b2a+3(−b)2(−c)+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
More Steps

Evaluate
3(−b)2(−c)
Multiply the terms
3b2(−c)
Multiply the numbers
−3b2c
a3−b3−c3−3a2b−3a2c+3b2a−3b2c+3(−c)2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
a3−b3−c3−3a2b−3a2c+3b2a−3b2c+3c2a+3(−c)2(−b)+6a(−b)(−c)
Calculate
More Steps

Evaluate
3(−c)2(−b)
Multiply the terms
3c2(−b)
Multiply the numbers
−3c2b
a3−b3−c3−3a2b−3a2c+3b2a−3b2c+3c2a−3c2b+6a(−b)(−c)
Solution
More Steps

Evaluate
6a(−b)(−c)
Multiply the numbers
−6ab(−c)
Multiply the numbers
6abc
a3−b3−c3−3a2b−3a2c+3b2a−3b2c+3c2a−3c2b+6abc
Show Solution
