Basic Math Examples

Multiply (3a-1/3b)(a-1/4b)
Step 1
Combine fractions.
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Step 1.1
Combine and .
Step 1.2
Combine and .
Step 2
Expand using the FOIL Method.
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Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify and combine like terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Multiply by by adding the exponents.
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Step 3.1.1.1
Move .
Step 3.1.1.2
Multiply by .
Step 3.1.2
Multiply .
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Step 3.1.2.1
Multiply by .
Step 3.1.2.2
Combine and .
Step 3.1.2.3
Combine and .
Step 3.1.3
Remove unnecessary parentheses.
Step 3.1.4
Move to the left of .
Step 3.1.5
Move the negative in front of the fraction.
Step 3.1.6
Combine and .
Step 3.1.7
Multiply .
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Step 3.1.7.1
Multiply by .
Step 3.1.7.2
Multiply by .
Step 3.1.7.3
Multiply by .
Step 3.1.7.4
Raise to the power of .
Step 3.1.7.5
Raise to the power of .
Step 3.1.7.6
Use the power rule to combine exponents.
Step 3.1.7.7
Add and .
Step 3.1.7.8
Multiply by .
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
Multiply by .
Step 3.4.4
Multiply by .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
To write as a fraction with a common denominator, multiply by .
Step 3.7
Combine and .
Step 3.8
Combine the numerators over the common denominator.
Step 3.9
Combine the numerators over the common denominator.
Step 4
Simplify the numerator.
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Multiply by .
Step 4.4
Subtract from .
Step 4.5
Factor by grouping.
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Step 4.5.1
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 4.5.1.1
Reorder terms.
Step 4.5.1.2
Reorder and .
Step 4.5.1.3
Factor out of .
Step 4.5.1.4
Rewrite as plus
Step 4.5.1.5
Apply the distributive property.
Step 4.5.1.6
Move parentheses.
Step 4.5.2
Factor out the greatest common factor from each group.
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Step 4.5.2.1
Group the first two terms and the last two terms.
Step 4.5.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.5.3
Factor the polynomial by factoring out the greatest common factor, .