Question

Which polynomial expression represents a sum of cubes? (6 – s)(s2 + 6s + 36) (6 + s)(s2 – 6s – 36) (6 + s)(s2 – 6s + 36) (6 + s)(s2 + 6s + 36)

Answer 1

Answer:

(6 + s)(s² – 6s + 36)

Step-by-step explanation:

(6 – s)(s² + 6s + 36)

= 6s² + 36s + 216 - s³ - 6s² - 36s

= -s³ + 6³

= 6³ - s³

(6 + s)(s² – 6s – 36)

= 6s² – 36s – 216 + s³ – 6s² – 36s

= s³ - 72s - 6³

(6 + s)(s² – 6s + 36)

= 6s² – 36s + 216 + s³ – 6s² + 36s

=s³ + 216

= s³ + 6³

Sum of cubes

(6 + s)(s² – 6s + 36)

(6 + s)(s² + 6s + 36)

= 6s² + 36s + 216 +  s³ + 6s² + 36s

= s³ + 12s² + 72s + 6³

(6 + s)(s² – 6s + 36) is sum of cubes = s³ + 6³

Answer 2

C

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