Pre-Algebra Examples

Simplify ( square root of 7- square root of 13)( square root of 7+ square root of 13)
Step 1
Expand using the FOIL Method.
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Step 1.1
Apply the distributive property.
Step 1.2
Apply the distributive property.
Step 1.3
Apply the distributive property.
Step 2
Simplify and combine like terms.
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Step 2.1
Simplify each term.
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Step 2.1.1
Combine using the product rule for radicals.
Step 2.1.2
Multiply by .
Step 2.1.3
Rewrite as .
Step 2.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 2.1.5
Combine using the product rule for radicals.
Step 2.1.6
Multiply by .
Step 2.1.7
Multiply .
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Step 2.1.7.1
Combine using the product rule for radicals.
Step 2.1.7.2
Multiply by .
Step 2.1.8
Multiply .
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Step 2.1.8.1
Raise to the power of .
Step 2.1.8.2
Raise to the power of .
Step 2.1.8.3
Use the power rule to combine exponents.
Step 2.1.8.4
Add and .
Step 2.1.9
Rewrite as .
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Step 2.1.9.1
Use to rewrite as .
Step 2.1.9.2
Apply the power rule and multiply exponents, .
Step 2.1.9.3
Combine and .
Step 2.1.9.4
Cancel the common factor of .
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Step 2.1.9.4.1
Cancel the common factor.
Step 2.1.9.4.2
Rewrite the expression.
Step 2.1.9.5
Evaluate the exponent.
Step 2.1.10
Multiply by .
Step 2.2
Subtract from .
Step 2.3
Subtract from .
Step 2.4
Add and .