Simplify (3u^(1/2)-v^(1/2))(u^(1/2)-2v^(1/2))

Math
(3u12-v12)(u12-2v12)
Expand (3u12-v12)(u12-2v12) using the FOIL Method.
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Apply the distributive property.
3u12(u12-2v12)-v12(u12-2v12)
Apply the distributive property.
3u12u12+3u12(-2v12)-v12(u12-2v12)
Apply the distributive property.
3u12u12+3u12(-2v12)-v12u12-v12(-2v12)
3u12u12+3u12(-2v12)-v12u12-v12(-2v12)
Simplify and combine like terms.
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Simplify each term.
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Multiply u12 by u12 by adding the exponents.
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Move u12.
3(u12u12)+3u12(-2v12)-v12u12-v12(-2v12)
Use the power rule aman=am+n to combine exponents.
3u12+12+3u12(-2v12)-v12u12-v12(-2v12)
Combine the numerators over the common denominator.
3u1+12+3u12(-2v12)-v12u12-v12(-2v12)
Add 1 and 1.
3u22+3u12(-2v12)-v12u12-v12(-2v12)
Divide 2 by 2.
3u1+3u12(-2v12)-v12u12-v12(-2v12)
3u1+3u12(-2v12)-v12u12-v12(-2v12)
Simplify 3u1.
3u+3u12(-2v12)-v12u12-v12(-2v12)
Rewrite using the commutative property of multiplication.
3u+3⋅-2(u12v12)-v12u12-v12(-2v12)
Multiply 3 by -2.
3u-6(u12v12)-v12u12-v12(-2v12)
Rewrite using the commutative property of multiplication.
3u-6u12v12-v12u12-1⋅-2(v12v12)
Multiply v12 by v12 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
3u-6u12v12-v12u12-1⋅-2v12+12
Combine the numerators over the common denominator.
3u-6u12v12-v12u12-1⋅-2v1+12
Add 1 and 1.
3u-6u12v12-v12u12-1⋅-2v22
Divide 2 by 2.
3u-6u12v12-v12u12-1⋅-2v1
3u-6u12v12-v12u12-1⋅-2v1
Simplify -1⋅-2v1.
3u-6u12v12-v12u12-1⋅-2v
Multiply -1 by -2.
3u-6u12v12-v12u12+2v
3u-6u12v12-v12u12+2v
Subtract v12u12 from -6u12v12.
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Move v12.
3u-6u12v12-1u12v12+2v
Subtract u12v12 from -6u12v12.
3u-7u12v12+2v
3u-7u12v12+2v
3u-7u12v12+2v
Move -7u12v12.
3u+2v-7u12v12
Simplify (3u^(1/2)-v^(1/2))(u^(1/2)-2v^(1/2))

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