(3k^2+2)(k+5k^2)
Multiply it out, using the FOIL rule.
15 k^4 + 3 k^3 + 10k^2 + 2k.
You can also write it as
k(5x + 1)(3k^2 +2)
To simplify the expression (3k^2 + 2)(k + 5k^2), we can use the distributive property.
First, distribute the terms of the first binomial (3k^2 + 2) to the terms of the second binomial (k + 5k^2):
(3k^2 + 2)(k + 5k^2)
= 3k^2 * k + 3k^2 * 5k^2 + 2 * k + 2 * 5k^2
Simplifying each term:
= 3k^3 + 15k^4 + 2k + 10k^2
Now we just need to combine like terms if any. In this case, we have terms with the same exponent on k, namely k^3, k^4, k^2, and k, so we can add or subtract them accordingly:
= 15k^4 + 3k^3 + 10k^2 + 2k
Thus, the simplified expression is 15k^4 + 3k^3 + 10k^2 + 2k.