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