Simplify (q^2+4)(q^2-4)(q-2)+2q(q^3+8)

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(q2+4)(q2-4)(q-2)+2q(q3+8)
Simplify each term.
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Expand (q2+4)(q2-4) using the FOIL Method.
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Apply the distributive property.
(q2(q2-4)+4(q2-4))(q-2)+2q(q3+8)
Apply the distributive property.
(q2q2+q2⋅-4+4(q2-4))(q-2)+2q(q3+8)
Apply the distributive property.
(q2q2+q2⋅-4+4q2+4⋅-4)(q-2)+2q(q3+8)
(q2q2+q2⋅-4+4q2+4⋅-4)(q-2)+2q(q3+8)
Combine the opposite terms in q2q2+q2⋅-4+4q2+4⋅-4.
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Reorder the factors in the terms q2⋅-4 and 4q2.
(q2q2-4q2+4q2+4⋅-4)(q-2)+2q(q3+8)
Add -4q2 and 4q2.
(q2q2+0+4⋅-4)(q-2)+2q(q3+8)
Add q2q2 and 0.
(q2q2+4⋅-4)(q-2)+2q(q3+8)
(q2q2+4⋅-4)(q-2)+2q(q3+8)
Simplify each term.
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Multiply q2 by q2 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(q2+2+4⋅-4)(q-2)+2q(q3+8)
Add 2 and 2.
(q4+4⋅-4)(q-2)+2q(q3+8)
(q4+4⋅-4)(q-2)+2q(q3+8)
Multiply 4 by -4.
(q4-16)(q-2)+2q(q3+8)
(q4-16)(q-2)+2q(q3+8)
Expand (q4-16)(q-2) using the FOIL Method.
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Apply the distributive property.
q4(q-2)-16(q-2)+2q(q3+8)
Apply the distributive property.
q4q+q4⋅-2-16(q-2)+2q(q3+8)
Apply the distributive property.
q4q+q4⋅-2-16q-16⋅-2+2q(q3+8)
q4q+q4⋅-2-16q-16⋅-2+2q(q3+8)
Simplify each term.
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Multiply q4 by q by adding the exponents.
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Multiply q4 by q.
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Raise q to the power of 1.
q4q1+q4⋅-2-16q-16⋅-2+2q(q3+8)
Use the power rule aman=am+n to combine exponents.
q4+1+q4⋅-2-16q-16⋅-2+2q(q3+8)
q4+1+q4⋅-2-16q-16⋅-2+2q(q3+8)
Add 4 and 1.
q5+q4⋅-2-16q-16⋅-2+2q(q3+8)
q5+q4⋅-2-16q-16⋅-2+2q(q3+8)
Move -2 to the left of q4.
q5-2⋅q4-16q-16⋅-2+2q(q3+8)
Multiply -16 by -2.
q5-2q4-16q+32+2q(q3+8)
q5-2q4-16q+32+2q(q3+8)
Apply the distributive property.
q5-2q4-16q+32+2q⋅q3+2q⋅8
Multiply q by q3 by adding the exponents.
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Move q3.
q5-2q4-16q+32+2(q3q)+2q⋅8
Multiply q3 by q.
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Raise q to the power of 1.
q5-2q4-16q+32+2(q3q1)+2q⋅8
Use the power rule aman=am+n to combine exponents.
q5-2q4-16q+32+2q3+1+2q⋅8
q5-2q4-16q+32+2q3+1+2q⋅8
Add 3 and 1.
q5-2q4-16q+32+2q4+2q⋅8
q5-2q4-16q+32+2q4+2q⋅8
Multiply 8 by 2.
q5-2q4-16q+32+2q4+16q
q5-2q4-16q+32+2q4+16q
Combine the opposite terms in q5-2q4-16q+32+2q4+16q.
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Add -2q4 and 2q4.
q5-16q+32+0+16q
Add q5-16q+32 and 0.
q5-16q+32+16q
Add -16q and 16q.
q5+0+32
Add q5 and 0.
q5+32
q5+32
Simplify (q^2+4)(q^2-4)(q-2)+2q(q^3+8)

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