Question

Find the product.

(i) (x² − 5) (x + 5) + 25

(ii) (a² + 5) (b³ + 3) + 5

(iii) (t + s²) (t² − s)

Answer 1

(i) (x² − 5) (x + 5) + 25

= x² (x + 5) − 5 (x + 5) + 25

= x³ + 5x² − 5x − 25 + 25

= x³ + 5x² − 5x

(ii) (a² + 5) (b³ + 3) + 5

= a² (b³ + 3) + 5 (b³ + 3) + 5

= a²b³ + 3a² + 5b³ + 15 + 5

= a²b³ + 3a² + 5b³ + 20

(iii) (t + s²) (t² − s)

= t (t² − s) + s² (t² − s)

= t³ − st + s²t² − s³