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To multiply these two expressions, we will use the distributive property:
(4y^5 + 10)(4y^9 + 8y + 3) = 4y^5(4y^9 + 8y + 3) + 10(4y^9 + 8y + 3)
Now, we will distribute the terms:
= 16y^14 + 32y^6 + 12y^5 + 40y^9 + 80y + 30
Combining like terms, we get:
= 16y^14 + 40y^9 + 32y^6 + 12y^5 + 80y + 30
Therefore, (4y^5+10)(4y^9+8y+3) simplifies to 16y^14 + 40y^9 + 32y^6 + 12y^5 + 80y + 30.