Algebra Examples

Simplify (8-x^3)/(25x^2+100-100x)
Step 1
Simplify the numerator.
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Step 1.1
Rewrite as .
Step 1.2
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 1.3
Raise to the power of .
Step 2
Simplify the denominator.
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.1.4
Factor out of .
Step 2.1.5
Factor out of .
Step 2.2
Factor using the perfect square rule.
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Step 2.2.1
Rearrange terms.
Step 2.2.2
Rewrite as .
Step 2.2.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.2.4
Rewrite the polynomial.
Step 2.2.5
Factor using the perfect square trinomial rule , where and .
Step 3
Reduce the expression by cancelling the common factors.
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Step 3.1
Cancel the common factor of and .
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Step 3.1.1
Rewrite as .
Step 3.1.2
Factor out of .
Step 3.1.3
Factor out of .
Step 3.1.4
Reorder terms.
Step 3.1.5
Factor out of .
Step 3.1.6
Cancel the common factors.
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Step 3.1.6.1
Factor out of .
Step 3.1.6.2
Cancel the common factor.
Step 3.1.6.3
Rewrite the expression.
Step 3.2
Move the negative in front of the fraction.