Question

К5(к+1)-(3+к2)(к4-3к2+9)

Answer 1

k^5(k+1)-(3+k²)(k^4-3k²+9)=

=k^5(k+1)-(k²+3)(k^4-3k²+9)=

=k^5(k+1)-(k^6-3³=

=k^5(k+1)-(k^6-27=

=k^6+k^5-k^6+27=

=k^5+27

Answer 2

To simplify the given expression, let's first expand the terms:

K5(k + 1) - (3 + k2)(k4 - 3k2 + 9)

Expanding the first term (K5(k + 1)): K5k + K5

Now, expanding the second term ((3 + k2)(k4 - 3k2 + 9)): Use the distributive property (FOIL method): (3 + k2)(k4) - (3 + k2)(3k2) + (3 + k2)(9)

Expand each part: 3k4 + k6 - 9k2 + 3k2 + 9k + 27

Now, let's put everything together and simplify the expression: K5k + K5 - (3k4 + k6 - 9k2 + 3k2 + 9k + 27)

Next, combine like terms: k6 + K5k - 3k4 - 6k2 + 9k + (K5 - 27)

So, the simplified expression is: k6 + K5k - 3k4 - 6k2 + 9k + (K5 - 27)