Chemistry Examples

Simplify (x-3-i)(x-3+i)(x-4i)(x+4i)
Step 1
Expand by multiplying each term in the first expression by each term in the second expression.
Step 2
Simplify terms.
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Step 2.1
Combine the opposite terms in .
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Step 2.1.1
Reorder the factors in the terms and .
Step 2.1.2
Subtract from .
Step 2.1.3
Add and .
Step 2.2
Simplify each term.
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Step 2.2.1
Multiply by .
Step 2.2.2
Move to the left of .
Step 2.2.3
Multiply by .
Step 2.2.4
Multiply by .
Step 2.2.5
Multiply .
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Step 2.2.5.1
Raise to the power of .
Step 2.2.5.2
Raise to the power of .
Step 2.2.5.3
Use the power rule to combine exponents.
Step 2.2.5.4
Add and .
Step 2.2.6
Rewrite as .
Step 2.2.7
Multiply by .
Step 2.3
Simplify by adding terms.
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Step 2.3.1
Combine the opposite terms in .
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Step 2.3.1.1
Add and .
Step 2.3.1.2
Add and .
Step 2.3.2
Subtract from .
Step 2.3.3
Add and .
Step 3
Expand by multiplying each term in the first expression by each term in the second expression.
Step 4
Simplify each term.
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Step 4.1
Multiply by by adding the exponents.
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Step 4.1.1
Multiply by .
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Step 4.1.1.1
Raise to the power of .
Step 4.1.1.2
Use the power rule to combine exponents.
Step 4.1.2
Add and .
Step 4.2
Multiply by by adding the exponents.
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Step 4.2.1
Move .
Step 4.2.2
Multiply by .
Step 4.3
Multiply by .
Step 4.4
Multiply by .
Step 5
Expand by multiplying each term in the first expression by each term in the second expression.
Step 6
Simplify terms.
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Step 6.1
Simplify each term.
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Step 6.1.1
Multiply by by adding the exponents.
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Step 6.1.1.1
Multiply by .
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Step 6.1.1.1.1
Raise to the power of .
Step 6.1.1.1.2
Use the power rule to combine exponents.
Step 6.1.1.2
Add and .
Step 6.1.2
Move to the left of .
Step 6.1.3
Multiply by by adding the exponents.
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Step 6.1.3.1
Move .
Step 6.1.3.2
Multiply by .
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Step 6.1.3.2.1
Raise to the power of .
Step 6.1.3.2.2
Use the power rule to combine exponents.
Step 6.1.3.3
Add and .
Step 6.1.4
Multiply .
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Step 6.1.4.1
Multiply by .
Step 6.1.4.2
Raise to the power of .
Step 6.1.4.3
Raise to the power of .
Step 6.1.4.4
Use the power rule to combine exponents.
Step 6.1.4.5
Add and .
Step 6.1.5
Rewrite as .
Step 6.1.6
Multiply by .
Step 6.1.7
Move to the left of .
Step 6.1.8
Multiply by by adding the exponents.
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Step 6.1.8.1
Move .
Step 6.1.8.2
Multiply by .
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Step 6.1.8.2.1
Raise to the power of .
Step 6.1.8.2.2
Use the power rule to combine exponents.
Step 6.1.8.3
Add and .
Step 6.1.9
Multiply by .
Step 6.1.10
Multiply by by adding the exponents.
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Step 6.1.10.1
Move .
Step 6.1.10.2
Multiply by .
Step 6.1.11
Multiply .
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Step 6.1.11.1
Multiply by .
Step 6.1.11.2
Raise to the power of .
Step 6.1.11.3
Raise to the power of .
Step 6.1.11.4
Use the power rule to combine exponents.
Step 6.1.11.5
Add and .
Step 6.1.12
Rewrite as .
Step 6.1.13
Multiply by .
Step 6.1.14
Multiply by by adding the exponents.
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Step 6.1.14.1
Move .
Step 6.1.14.2
Multiply by .
Step 6.1.15
Multiply by .
Step 6.1.16
Multiply .
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Step 6.1.16.1
Multiply by .
Step 6.1.16.2
Raise to the power of .
Step 6.1.16.3
Raise to the power of .
Step 6.1.16.4
Use the power rule to combine exponents.
Step 6.1.16.5
Add and .
Step 6.1.17
Rewrite as .
Step 6.1.18
Multiply by .
Step 6.2
Simplify by adding terms.
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Step 6.2.1
Combine the opposite terms in .
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Step 6.2.1.1
Reorder the factors in the terms and .
Step 6.2.1.2
Subtract from .
Step 6.2.1.3
Add and .
Step 6.2.1.4
Add and .
Step 6.2.1.5
Add and .
Step 6.2.1.6
Reorder the factors in the terms and .
Step 6.2.1.7
Subtract from .
Step 6.2.1.8
Add and .
Step 6.2.2
Add and .
Step 6.2.3
Move .