Question
Simplify the expression
4096b2c2+256b4c2+256c4b2−2048b3c2−2048c3b2+512b3c3
Evaluate
(4−b−c)2×16b2×16c2
Multiply the terms
(4−b−c)2×256b2c2
Use the commutative property to reorder the terms
256(4−b−c)2b2c2
Evaluate the power
More Steps

Evaluate
(4−b−c)2
Use (a+b+c)2=a2+b2+c2+2ab+2ac+2bc to expand the expression
42+(−b)2+(−c)2+2×4(−b)+2×4(−c)+2(−b)(−c)
Calculate
16+(−b)2+(−c)2+2×4(−b)+2×4(−c)+2(−b)(−c)
Calculate
16+b2+(−c)2+2×4(−b)+2×4(−c)+2(−b)(−c)
Calculate
16+b2+c2+2×4(−b)+2×4(−c)+2(−b)(−c)
Calculate
More Steps

Evaluate
2×4(−b)
Multiply the numbers
8(−b)
Multiply the numbers
−8b
16+b2+c2−8b+2×4(−c)+2(−b)(−c)
Calculate
More Steps

Evaluate
2×4(−c)
Multiply the numbers
8(−c)
Multiply the numbers
−8c
16+b2+c2−8b−8c+2(−b)(−c)
Calculate
More Steps

Evaluate
2(−b)(−c)
Multiply the numbers
−2b(−c)
Multiply the numbers
2bc
16+b2+c2−8b−8c+2bc
256(16+b2+c2−8b−8c+2bc)b2c2
Multiply the terms
More Steps

Evaluate
256(16+b2+c2−8b−8c+2bc)
Apply the distributive property
256×16+256b2+256c2−256×8b−256×8c+256×2bc
Multiply the numbers
4096+256b2+256c2−256×8b−256×8c+256×2bc
Multiply the numbers
4096+256b2+256c2−2048b−256×8c+256×2bc
Multiply the numbers
4096+256b2+256c2−2048b−2048c+256×2bc
Multiply the numbers
4096+256b2+256c2−2048b−2048c+512bc
(4096+256b2+256c2−2048b−2048c+512bc)b2c2
Multiply the terms
More Steps

Evaluate
(4096+256b2+256c2−2048b−2048c+512bc)b2
Apply the distributive property
4096b2+256b2×b2+256c2b2−2048b×b2−2048cb2+512bcb2
Multiply the terms
More Steps

Evaluate
b2×b2
Use the product rule an×am=an+m to simplify the expression
b2+2
Add the numbers
b4
4096b2+256b4+256c2b2−2048b×b2−2048cb2+512bcb2
Multiply the terms
More Steps

Evaluate
b×b2
Use the product rule an×am=an+m to simplify the expression
b1+2
Add the numbers
b3
4096b2+256b4+256c2b2−2048b3−2048cb2+512bcb2
Multiply the terms
More Steps

Evaluate
b×b2
Use the product rule an×am=an+m to simplify the expression
b1+2
Add the numbers
b3
4096b2+256b4+256c2b2−2048b3−2048cb2+512b3c
(4096b2+256b4+256c2b2−2048b3−2048cb2+512b3c)c2
Apply the distributive property
4096b2c2+256b4c2+256c2b2c2−2048b3c2−2048cb2c2+512b3c×c2
Multiply the terms
More Steps

Evaluate
c2×c2
Use the product rule an×am=an+m to simplify the expression
c2+2
Add the numbers
c4
4096b2c2+256b4c2+256c4b2−2048b3c2−2048cb2c2+512b3c×c2
Multiply the terms
More Steps

Evaluate
c×c2
Use the product rule an×am=an+m to simplify the expression
c1+2
Add the numbers
c3
4096b2c2+256b4c2+256c4b2−2048b3c2−2048c3b2+512b3c×c2
Solution
More Steps

Evaluate
c×c2
Use the product rule an×am=an+m to simplify the expression
c1+2
Add the numbers
c3
4096b2c2+256b4c2+256c4b2−2048b3c2−2048c3b2+512b3c3
Show Solution
