(i) (x^{2} − 5) (x + 5) + 25

= x^{2} (x + 5) − 5 (x + 5) + 25

= x^{3} + 5x^{2} − 5x − 25 + 25

= x^{3} + 5x^{2} − 5x

(ii) (a^{2 }+ 5) (b^{3} + 3) + 5

= a^{2} (b^{3} + 3) + 5 (b^{3} + 3) + 5

= a^{2}b^{3} + 3a^{2} + 5b^{3} + 15 + 5

= a^{2}b^{3} + 3a^{2} + 5b^{3} + 20

(iii) (t + s^{2}) (t^{2} − s)

= t (t^{2} − s) + s^{2 }(t^{2} − s)

= t^{3} − st + s^{2}t^{2} − s^{3}