Respuesta :

Answer:

The form of the sum of cubes identity is a³ + b³ = (a + b)(a² - ab + b²)A

Step-by-step explanation:

To find the form of the sum of cubes identity ⇒ x³ + y³

  1. find the cube root of each one and add them in a small bracket ⇒ (x + y)
  2. square the first term in the small bracket and put it as the 1st term in a big bracket ⇒ (x² ....)
  3. put (-) after the 1st term ⇒ (x² - .....)
  4. multiply the 1st and 2nd term in the small bracket and put the product as the 2nd term in the big bracket ⇒ (x² - xy .....)
  5. square the 2nd term in the small bracket and add it to the terms of the big bracket ⇒ (x² - xy + y²)

Then the form of the sum of cubes identity is x³ + y³ = (x + y)(x² - xy + y²)

a³ + b³ is a sum of two cubes

→ By using the same steps above

∵ [tex]\sqrt[3]{a^{3}}[/tex] = a and  [tex]\sqrt[3]{b^{3}}[/tex] = b

The small bracket is (a + b)

∵ Square a = a² and square b = b²

∵ a × b = ab

The big bracket is (a² - ab + b²)

The form of the sum of cubes identity is a³ + b³ = (a + b)(a² - ab + b²)

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