Multiply (3a-1/3b)(a-1/4b)

Math
(3a-13b)(a-14b)
Combine fractions.
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Combine b and 13.
(3a-b3)(a-14b)
Combine b and 14.
(3a-b3)(a-b4)
(3a-b3)(a-b4)
Expand (3a-b3)(a-b4) using the FOIL Method.
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Apply the distributive property.
3a(a-b4)-b3(a-b4)
Apply the distributive property.
3a⋅a+3a(-b4)-b3(a-b4)
Apply the distributive property.
3a⋅a+3a(-b4)-b3a-b3(-b4)
3a⋅a+3a(-b4)-b3a-b3(-b4)
Simplify and combine like terms.
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Simplify each term.
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Multiply a by a by adding the exponents.
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Move a.
3(a⋅a)+3a(-b4)-b3a-b3(-b4)
Multiply a by a.
3a2+3a(-b4)-b3a-b3(-b4)
3a2+3a(-b4)-b3a-b3(-b4)
Multiply 3a(-b4).
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Multiply -1 by 3.
3a2-3ab4-b3a-b3(-b4)
Combine -3 and b4.
3a2+a-3b4-b3a-b3(-b4)
Combine a and -3b4.
3a2+a(-3b)4-b3a-b3(-b4)
3a2+a(-3b)4-b3a-b3(-b4)
Move -3 to the left of a.
3a2+-3⋅ab4-b3a-b3(-b4)
Move the negative in front of the fraction.
3a2-(3)⋅ab4-b3a-b3(-b4)
Combine a and b3.
3a2-3ab4-ab3-b3(-b4)
Multiply -b3(-b4).
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Multiply -1 by -1.
3a2-3ab4-ab3+1b3b4
Multiply b3 by 1.
3a2-3ab4-ab3+b3⋅b4
Multiply b3 and b4.
3a2-3ab4-ab3+b⋅b3⋅4
Raise b to the power of 1.
3a2-3ab4-ab3+b1b3⋅4
Raise b to the power of 1.
3a2-3ab4-ab3+b1b13⋅4
Use the power rule aman=am+n to combine exponents.
3a2-3ab4-ab3+b1+13⋅4
Add 1 and 1.
3a2-3ab4-ab3+b23⋅4
Multiply 3 by 4.
3a2-3ab4-ab3+b212
3a2-3ab4-ab3+b212
3a2-3ab4-ab3+b212
To write -3ab4 as a fraction with a common denominator, multiply by 33.
3a2-3ab4⋅33-ab3+b212
To write -ab3 as a fraction with a common denominator, multiply by 44.
3a2-3ab4⋅33-ab3⋅44+b212
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
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Multiply 3ab4 and 33.
3a2-3ab⋅34⋅3-ab3⋅44+b212
Multiply 4 by 3.
3a2-3ab⋅312-ab3⋅44+b212
Multiply ab3 and 44.
3a2-3ab⋅312-ab⋅43⋅4+b212
Multiply 3 by 4.
3a2-3ab⋅312-ab⋅412+b212
3a2-3ab⋅312-ab⋅412+b212
Combine the numerators over the common denominator.
3a2+-3ab⋅3-ab⋅412+b212
To write 3a2 as a fraction with a common denominator, multiply by 1212.
3a2⋅1212+-3ab⋅3-ab⋅412+b212
Combine 3a2 and 1212.
3a2⋅1212+-3ab⋅3-ab⋅412+b212
Combine the numerators over the common denominator.
3a2⋅12-3ab⋅3-ab⋅412+b212
Combine the numerators over the common denominator.
3a2⋅12-3ab⋅3-ab⋅4+b212
3a2⋅12-3ab⋅3-ab⋅4+b212
Simplify the numerator.
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Multiply 12 by 3.
36a2-3ab⋅3-ab⋅4+b212
Multiply 3 by -3.
36a2-9ab-ab⋅4+b212
Multiply 4 by -1.
36a2-9ab-4ab+b212
Subtract 4ab from -9ab.
36a2-13ab+b212
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=36⋅1=36 and whose sum is b=-13.
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Reorder terms.
36a2+b2-13ab12
Reorder b2 and -13ab.
36a2-13ab+b212
Factor -13 out of -13ab.
36a2-13(ab)+b212
Rewrite -13 as -4 plus -9
36a2+(-4-9)(ab)+b212
Apply the distributive property.
36a2-4(ab)-9(ab)+b212
Move parentheses.
36a2-4ab-9ab+b212
36a2-4ab-9ab+b212
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(36a2-4ab)-9ab+b212
Factor out the greatest common factor (GCF) from each group.
4a(9a-b)-b(9a-b)12
4a(9a-b)-b(9a-b)12
Factor the polynomial by factoring out the greatest common factor, 9a-b.
(9a-b)(4a-b)12
(9a-b)(4a-b)12
(9a-b)(4a-b)12
Multiply (3a-1/3b)(a-1/4b)

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