Algebra Examples

Solve by Factoring x^4-41x^2+400=0
Step 1
Rewrite as .
Step 2
Let . Substitute for all occurrences of .
Step 3
Factor using the AC method.
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Step 3.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2
Write the factored form using these integers.
Step 4
Replace all occurrences of with .
Step 5
Rewrite as .
Step 6
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 7
Rewrite as .
Step 8
Factor.
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Step 8.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 8.2
Remove unnecessary parentheses.
Step 9
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 10
Set equal to and solve for .
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Step 10.1
Set equal to .
Step 10.2
Subtract from both sides of the equation.
Step 11
Set equal to and solve for .
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Step 11.1
Set equal to .
Step 11.2
Add to both sides of the equation.
Step 12
Set equal to and solve for .
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Step 12.1
Set equal to .
Step 12.2
Subtract from both sides of the equation.
Step 13
Set equal to and solve for .
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Step 13.1
Set equal to .
Step 13.2
Add to both sides of the equation.
Step 14
The final solution is all the values that make true.