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Algebra Examples
Step 1
Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
Step 1.3.1
Simplify each term.
Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Multiply by .
Step 1.3.1.3
Multiply by .
Step 1.3.1.4
Multiply by .
Step 1.3.2
Add and .
Step 2
Subtract from .
Step 3
The minimum of a quadratic function occurs at . If is positive, the minimum value of the function is .
occurs at
Step 4
Step 4.1
Substitute in the values of and .
Step 4.2
Remove parentheses.
Step 4.3
Simplify .
Step 4.3.1
Cancel the common factor of .
Step 4.3.1.1
Cancel the common factor.
Step 4.3.1.2
Rewrite the expression.
Step 4.3.2
Multiply by .
Step 5
Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
Step 5.2.1
Simplify each term.
Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Multiply by .
Step 5.2.2
Simplify by subtracting numbers.
Step 5.2.2.1
Subtract from .
Step 5.2.2.2
Subtract from .
Step 5.2.3
The final answer is .
Step 6
Use the and values to find where the minimum occurs.
Step 7