Simplify (a+b+c)(b+c-a)

Math
(a+b+c)(b+c-a)
Expand (a+b+c)(b+c-a) by multiplying each term in the first expression by each term in the second expression.
ab+ac+a(-a)+b⋅b+bc+b(-a)+cb+c⋅c+c(-a)
Simplify terms.
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Combine the opposite terms in ab+ac+a(-a)+b⋅b+bc+b(-a)+cb+c⋅c+c(-a).
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Reorder the factors in the terms ab and b(-a).
ab+ac+a(-a)+b⋅b+bc-ab+cb+c⋅c+c(-a)
Subtract ab from ab.
ac+a(-a)+b⋅b+bc+0+cb+c⋅c+c(-a)
Add ac+a(-a)+b⋅b+bc and 0.
ac+a(-a)+b⋅b+bc+cb+c⋅c+c(-a)
Reorder the factors in the terms ac and c(-a).
ac+a(-a)+b⋅b+bc+cb+c⋅c-ac
Subtract ac from ac.
a(-a)+b⋅b+bc+cb+c⋅c+0
Add a(-a)+b⋅b+bc+cb+c⋅c and 0.
a(-a)+b⋅b+bc+cb+c⋅c
a(-a)+b⋅b+bc+cb+c⋅c
Simplify each term.
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Rewrite using the commutative property of multiplication.
-a⋅a+b⋅b+bc+cb+c⋅c
Multiply a by a by adding the exponents.
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Move a.
-(a⋅a)+b⋅b+bc+cb+c⋅c
Multiply a by a.
-a2+b⋅b+bc+cb+c⋅c
-a2+b⋅b+bc+cb+c⋅c
Multiply b by b.
-a2+b2+bc+cb+c⋅c
Multiply c by c.
-a2+b2+bc+cb+c2
-a2+b2+bc+cb+c2
-a2+b2+bc+cb+c2
Add bc and cb.
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Reorder c and b.
-a2+b2+bc+bc+c2
Add bc and bc.
-a2+b2+2bc+c2
-a2+b2+2bc+c2
Simplify (a+b+c)(b+c-a)

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