# Simplify (4a-b+2c)^2

(4a-b+2c)2
Rewrite (4a-b+2c)2 as (4a-b+2c)(4a-b+2c).
(4a-b+2c)(4a-b+2c)
Expand (4a-b+2c)(4a-b+2c) by multiplying each term in the first expression by each term in the second expression.
4a(4a)+4a(-b)+4a(2c)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Simplify each term.
Multiply a by a.
4⋅4a2+4a(-b)+4a(2c)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply 4 by 4.
16a2+4a(-b)+4a(2c)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2+4⋅-1(ab)+4a(2c)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply 4 by -1.
16a2-4(ab)+4a(2c)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2-4ab+4⋅2(ac)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply 4 by 2.
16a2-4ab+8(ac)-b(4a)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2-4ab+8ac-1⋅4(ba)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply -1 by 4.
16a2-4ab+8ac-4(ba)-b(-b)-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply b by b.
16a2-4ab+8ac-4ba-1⋅-1b2-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply -1 by -1.
16a2-4ab+8ac-4ba+1b2-b(2c)+2c(4a)+2c(-b)+2c(2c)
Multiply b2 by 1.
16a2-4ab+8ac-4ba+b2-b(2c)+2c(4a)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2-4ab+8ac-4ba+b2-1⋅2(bc)+2c(4a)+2c(-b)+2c(2c)
Multiply -1 by 2.
16a2-4ab+8ac-4ba+b2-2(bc)+2c(4a)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2-4ab+8ac-4ba+b2-2bc+2⋅4(ca)+2c(-b)+2c(2c)
Multiply 2 by 4.
16a2-4ab+8ac-4ba+b2-2bc+8(ca)+2c(-b)+2c(2c)
Rewrite using the commutative property of multiplication.
16a2-4ab+8ac-4ba+b2-2bc+8ca+2⋅-1(cb)+2c(2c)
Multiply 2 by -1.
16a2-4ab+8ac-4ba+b2-2bc+8ca-2(cb)+2c(2c)
Multiply c by c.
16a2-4ab+8ac-4ba+b2-2bc+8ca-2cb+2⋅2c2
Multiply 2 by 2.
16a2-4ab+8ac-4ba+b2-2bc+8ca-2cb+4c2
16a2-4ab+8ac-4ba+b2-2bc+8ca-2cb+4c2
Subtract 4ba from -4ab.
Move b.
16a2-4ab-4ab+8ac+b2-2bc+8ca-2cb+4c2
Subtract 4ab from -4ab.
16a2-8ab+8ac+b2-2bc+8ca-2cb+4c2
16a2-8ab+8ac+b2-2bc+8ca-2cb+4c2
Move c.
16a2-8ab+b2-2bc+8ac+8ac-2cb+4c2
16a2-8ab+b2-2bc+16ac-2cb+4c2
16a2-8ab+b2-2bc+16ac-2cb+4c2
Subtract 2cb from -2bc.
Move c.
16a2-8ab+b2-2bc-2bc+16ac+4c2
Subtract 2bc from -2bc.
16a2-8ab+b2-4bc+16ac+4c2
16a2-8ab+b2-4bc+16ac+4c2
Move -4bc.
16a2-8ab+b2+16ac-4bc+4c2
Move b2.
16a2-8ab+16ac+b2-4bc+4c2
Simplify (4a-b+2c)^2

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