Trigonometry Examples

Solve for x (a+b)(a-b)=a^2-b^2
Step 1
Simplify .
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Step 1.1
Rewrite.
Step 1.2
Simplify by adding zeros.
Step 1.3
Expand using the FOIL Method.
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Step 1.3.1
Apply the distributive property.
Step 1.3.2
Apply the distributive property.
Step 1.3.3
Apply the distributive property.
Step 1.4
Simplify terms.
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Step 1.4.1
Combine the opposite terms in .
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Step 1.4.1.1
Reorder the factors in the terms and .
Step 1.4.1.2
Add and .
Step 1.4.1.3
Add and .
Step 1.4.2
Simplify each term.
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Step 1.4.2.1
Multiply by .
Step 1.4.2.2
Rewrite using the commutative property of multiplication.
Step 1.4.2.3
Multiply by by adding the exponents.
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Step 1.4.2.3.1
Move .
Step 1.4.2.3.2
Multiply by .
Step 2
Move all terms containing to the left side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Combine the opposite terms in .
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Step 2.2.1
Subtract from .
Step 2.2.2
Add and .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Dividing two negative values results in a positive value.
Step 3.2.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Dividing two negative values results in a positive value.
Step 3.3.2
Divide by .
Step 4
Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.
Step 5
Solve for .
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Step 5.1
Rewrite the absolute value equation as four equations without absolute value bars.
Step 5.2
After simplifying, there are only two unique equations to be solved.
Step 5.3
Solve for .
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Step 5.3.1
Move all terms containing to the left side of the equation.
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Step 5.3.1.1
Subtract from both sides of the equation.
Step 5.3.1.2
Subtract from .
Step 5.3.2
Since , the equation will always be true.
Always true
Always true
Step 5.4
Solve for .
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Step 5.4.1
Move all terms containing to the left side of the equation.
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Step 5.4.1.1
Add to both sides of the equation.
Step 5.4.1.2
Add and .
Step 5.4.2
Divide each term in by and simplify.
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Step 5.4.2.1
Divide each term in by .
Step 5.4.2.2
Simplify the left side.
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Step 5.4.2.2.1
Cancel the common factor of .
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Step 5.4.2.2.1.1
Cancel the common factor.
Step 5.4.2.2.1.2
Divide by .
Step 5.4.2.3
Simplify the right side.
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Step 5.4.2.3.1
Divide by .
Step 5.5
List all of the solutions.