Question

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Answer 1

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

∵ $\sqrt[3]{a^{3}}$ = a and  $\sqrt[3]{b^{3}}$ = 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)