Precalculus Examples

Step 1
Simplify with factoring out.
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Step 1.1
Reorder and .
Step 1.2
Rewrite as .
Step 1.3
Factor out of .
Step 1.4
Factor out of .
Step 1.5
Rewrite as .
Step 2
Apply pythagorean identity.
Step 3
Simplify terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Rewrite in terms of sines and cosines.
Step 3.1.2
Apply the product rule to .
Step 3.2
Apply the distributive property.
Step 4
Multiply .
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Step 4.1
Combine and .
Step 4.2
Multiply by by adding the exponents.
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Step 4.2.1
Use the power rule to combine exponents.
Step 4.2.2
Add and .
Step 5
Multiply .
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 6
Simplify the expression.
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Step 6.1
Rewrite as .
Step 6.2
Reorder and .
Step 7
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 8
Simplify terms.
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Step 8.1
Simplify each term.
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Step 8.1.1
Factor out of .
Step 8.1.2
Separate fractions.
Step 8.1.3
Convert from to .
Step 8.1.4
Divide by .
Step 8.2
Simplify each term.
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Step 8.2.1
Factor out of .
Step 8.2.2
Separate fractions.
Step 8.2.3
Convert from to .
Step 8.2.4
Divide by .
Step 9
Expand using the FOIL Method.
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Step 9.1
Apply the distributive property.
Step 9.2
Apply the distributive property.
Step 9.3
Apply the distributive property.
Step 10
Simplify terms.
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Step 10.1
Combine the opposite terms in .
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Step 10.1.1
Reorder the factors in the terms and .
Step 10.1.2
Add and .
Step 10.1.3
Add and .
Step 10.2
Simplify each term.
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Step 10.2.1
Multiply .
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Step 10.2.1.1
Raise to the power of .
Step 10.2.1.2
Raise to the power of .
Step 10.2.1.3
Use the power rule to combine exponents.
Step 10.2.1.4
Add and .
Step 10.2.2
Rewrite using the commutative property of multiplication.
Step 10.2.3
Multiply .
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Step 10.2.3.1
Raise to the power of .
Step 10.2.3.2
Raise to the power of .
Step 10.2.3.3
Use the power rule to combine exponents.
Step 10.2.3.4
Add and .
Step 10.2.4
Multiply .
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Step 10.2.4.1
Raise to the power of .
Step 10.2.4.2
Raise to the power of .
Step 10.2.4.3
Use the power rule to combine exponents.
Step 10.2.4.4
Add and .
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