Studdy Solution
STEP 1
Assumptions1. a, b, and c are real numbers.
STEP 2
We will first expand the squares in the given expression.
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca(a−b−c)2=a2+b2+c2−2ab−2bc+2ca
STEP 3
Substitute these expanded forms back into the original expression.
a2+b2+c2+2ab+2bc+2ca−(a2+b2+c2−2ab−2bc+2ca)−ab
STEP 4
implify the expression by combining like terms.
2ab+2bc+2ca−(−2ab−2bc+2ca)−4ab
STEP 5
Further simplify the expression.
2ab+2bc+2ca+2ab+2bc−2ca−4ab
STEP 6
Combine like terms.
4ab+4bc−4ab
STEP 7
implify the expression.
4bcSo, (a+b+c)2−(a−b−c)2−4ab=4bc.