Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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Question: 1 / 400

What is the factored form of a³ + b³?

(a+b)(a²-ab+b²)

To factor the expression $a^3 + b^3$, you can apply the sum of cubes formula. The sum of cubes states that for any two terms $x$ and $y$, the expression $x^3 + y^3$ can be factored as:

x^3 + y^3 = (x + y)(x^2 - xy + y^2).

In this case, let $x = a$ and $y = b$. Applying the sum of cubes formula gives:

a^3 + b^3 = (a + b)(a^2 - ab + b^2).

The first part of the factorization $ (a + b) $ indicates that when the cubes $a^3$ and $b^3$ are summed, they can be grouped based on their linear factors, leading to $ a + b $.

The second part $ (a^2 - ab + b^2) $ is a quadratic expression representing the remaining factors after factoring out $ (a + b) $. This expression ensures that the factors will return to the original cubic form when multiplied out.

Thus, the

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(a-b)(a²+ab+b²)

(a+b)(c+d)

(y₂-y₁)/(x₂-x₁)

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