multiply and check
(a^2+4)(5a^3-3a-1)
To multiply the expressions (a^2+4) and (5a^3-3a-1), you can use the distributive property. Here are the steps to follow:
Step 1: Multiply each term of the first expression (a^2+4) by each term of the second expression (5a^3-3a-1).
(a^2+4) * (5a^3-3a-1) =
(a^2 * 5a^3) + (a^2 * -3a) + (a^2 * -1) +
(4 * 5a^3) + (4 * -3a) + (4 * -1)
Step 2: Simplify each term.
(a^2 * 5a^3) = 5a^5
(a^2 * -3a) = -3a^3
(a^2 * -1) = -a^2
(4 * 5a^3) = 20a^3
(4 * -3a) = -12a
(4 * -1) = -4
Step 3: Combine like terms by adding or subtracting.
5a^5 + (-3a^3) + (-a^2) + 20a^3 + (-12a) + (-4)
Step 4: Simplify further if possible.
5a^5 + 17a^3 - a^2 - 12a - 4
The simplified expression after multiplying is 5a^5 + 17a^3 - a^2 - 12a - 4.