Question

Consider the sum of cubes identity

a^3 +b^3 =(a+b)(a^2 -ab+b^2) for the polynomial 8x^3 +27, a= and b=​

Answer 1

a = 2x

b = 3

Explanation:

Consider the sum of cubes identity

a³ + b³ =(a + b)(a² -ab +b²)

for the polynomial 8x³ +27, we factorise

8x³ + 27

∛8 = 2

∛8 = x

∛27 = 3

Therefore, we can say that :

8x³ + 27 = (2x)³ + 3³

Using this: a³ + b³ =(a + b)(a² -ab +b²)

We can say that

a = 2x

b = 3

To confirm that: a = 2x and b = 3 we factorise 8x³ + 27

= (2x)³ + 3³

= (2x + 3)((2x)²− 2x × 3 + 3²)

= (2x + 3)(4x² - 6x + 9)

= 8x³ - 12x² +18x + 12x² - 18x + 27

= 8x³ + 27

Therefore, a = 2x and b = 3 is correct.

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