Basic Math Examples

Simplify (a(3a+b)(2a-9b)a)/(b*b*(b(a+5b)))*(5ab-20b^2)/(a^2-9ab+20b^2)
Step 1
Simplify the numerator.
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Step 1.1
Raise to the power of .
Step 1.2
Raise to the power of .
Step 1.3
Use the power rule to combine exponents.
Step 1.4
Add and .
Step 2
Simplify the denominator.
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Step 2.1
Raise to the power of .
Step 2.2
Raise to the power of .
Step 2.3
Use the power rule to combine exponents.
Step 2.4
Add and .
Step 2.5
Multiply by by adding the exponents.
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Step 2.5.1
Move .
Step 2.5.2
Multiply by .
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Step 2.5.2.1
Raise to the power of .
Step 2.5.2.2
Use the power rule to combine exponents.
Step 2.5.3
Add and .
Step 3
Factor out of .
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Step 3.1
Factor out of .
Step 3.2
Factor out of .
Step 3.3
Factor out of .
Step 4
Factor by grouping.
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Step 4.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 4.1.1
Reorder terms.
Step 4.1.2
Reorder and .
Step 4.1.3
Factor out of .
Step 4.1.4
Rewrite as plus
Step 4.1.5
Apply the distributive property.
Step 4.1.6
Move parentheses.
Step 4.2
Factor out the greatest common factor from each group.
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Step 4.2.1
Group the first two terms and the last two terms.
Step 4.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5
Combine.
Step 6
Cancel the common factor of and .
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Step 6.1
Factor out of .
Step 6.2
Cancel the common factors.
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Step 6.2.1
Factor out of .
Step 6.2.2
Cancel the common factor.
Step 6.2.3
Rewrite the expression.
Step 7
Cancel the common factor of .
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Step 7.1
Cancel the common factor.
Step 7.2
Rewrite the expression.
Step 8
Move to the left of .