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Karolina [17]
3 years ago
8

Which polynomial identity will prove that 19 = 27 − 8?

Mathematics
1 answer:
3241004551 [841]3 years ago
5 0
The answer is Difference of Cubes.

Difference of cubes is a³ - b³.
27 can be written as 3³ (= 3 × 3 × 3 = 27). So, a = 3.
8 can be written as 2³ (= 2 × 2 × 2 = 8). So, b = 2.

Difference of cubes can be expressed as:
       a³ - b³ = (a - b)(a² + ab + b²)
⇒   3³ - 2³ = (3 - 2)(3² + 3×2 + 2²) = 1 × (9 + 6 + 4) = 1 × 19 = 19
⇒  27 -  8  = 19


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