It can be inferred that the question seeks an explanation for the sum of cubes which is given as a³ + b³. This formula is known as the sum of cubes.
This formula is used to find the sum of two cubes without calculating the geometrical values of each cube. It is also used as a formula for factorizing the binomials of cubes.
The above formula can be verified by finding the product of (a + b) and (a2 - ab + b2)
Assuming that a³ + b³ = X; and
(a + b) (a2 - ab + b2) = Y, we state that X = Y.
To proof that X = Y
Step 1 - Expand Y
Multiplying the a and b with (a2 - ab + b2), we have:
= a (a² - ab + b²) + b(a² - ab + b²)
= a³ - a²b + ab² + a²b - ab² + b³
= a³ - a²b + a²b + ab²- ab² + b³
= a³ - 0 + 0 + b³
= a³ + b³
QED
Learn more about the sum of cubes at:
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