Multiply (4v^2+6v+3)(5v^2-6v+1)

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(4v2+6v+3)(5v2-6v+1)
Expand (4v2+6v+3)(5v2-6v+1) by multiplying each term in the first expression by each term in the second expression.
4v2(5v2)+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Simplify terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
4⋅5(v2v2)+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply v2 by v2 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
4⋅5v2+2+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Add 2 and 2.
4⋅5v4+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
4⋅5v4+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 4 by 5.
20v4+4v2(-6v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Rewrite using the commutative property of multiplication.
20v4+4⋅-6(v2v)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply v2 by v by adding the exponents.
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Multiply v2 by v.
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Raise v to the power of 1.
20v4+4⋅-6(v2v1)+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Use the power rule aman=am+n to combine exponents.
20v4+4⋅-6v2+1+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
20v4+4⋅-6v2+1+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Add 2 and 1.
20v4+4⋅-6v3+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
20v4+4⋅-6v3+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 4 by -6.
20v4-24v3+4v2⋅1+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 4 by 1.
20v4-24v3+4v2+6v(5v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Rewrite using the commutative property of multiplication.
20v4-24v3+4v2+6⋅5(v⋅v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply v by v2 by adding the exponents.
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Multiply v by v2.
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Raise v to the power of 1.
20v4-24v3+4v2+6⋅5(v1v2)+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Use the power rule aman=am+n to combine exponents.
20v4-24v3+4v2+6⋅5v1+2+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
20v4-24v3+4v2+6⋅5v1+2+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Add 1 and 2.
20v4-24v3+4v2+6⋅5v3+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
20v4-24v3+4v2+6⋅5v3+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 6 by 5.
20v4-24v3+4v2+30v3+6v(-6v)+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply v by v.
20v4-24v3+4v2+30v3+6⋅-6v2+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 6 by -6.
20v4-24v3+4v2+30v3-36v2+6v⋅1+3(5v2)+3(-6v)+3⋅1
Multiply 6 by 1.
20v4-24v3+4v2+30v3-36v2+6v+3(5v2)+3(-6v)+3⋅1
Multiply 5 by 3.
20v4-24v3+4v2+30v3-36v2+6v+15v2+3(-6v)+3⋅1
Multiply -6 by 3.
20v4-24v3+4v2+30v3-36v2+6v+15v2-18v+3⋅1
Multiply 3 by 1.
20v4-24v3+4v2+30v3-36v2+6v+15v2-18v+3
20v4-24v3+4v2+30v3-36v2+6v+15v2-18v+3
Simplify by adding terms.
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Add -24v3 and 30v3.
20v4+6v3+4v2-36v2+6v+15v2-18v+3
Subtract 36v2 from 4v2.
20v4+6v3-32v2+6v+15v2-18v+3
Add -32v2 and 15v2.
20v4+6v3-17v2+6v-18v+3
Subtract 18v from 6v.
20v4+6v3-17v2-12v+3
20v4+6v3-17v2-12v+3
20v4+6v3-17v2-12v+3
Multiply (4v^2+6v+3)(5v^2-6v+1)

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