How do you factor x³ + y³?
How do you factor x³ + y³?
Aniket Singh , 7 Months ago
Grade
10 grade maths> How do you factor x³ + y³?...
1 AnswersAskiitians Tutor Team
Factoring the expression \(x^3 + y^3\) can be accomplished using a specific formula for the sum of cubes. This formula states that:
Sum of Cubes Formula
The sum of cubes can be factored as follows:
a³ + b³ = (a + b)(a² - ab + b²)
Applying the Formula
In your case, let \(a = x\) and \(b = y\). Therefore, you can rewrite \(x^3 + y^3\) as:
x³ + y³ = (x + y)(x² - xy + y²)
Final Factored Form
So, the complete factorization of \(x^3 + y^3\) is:
- (x + y) - the sum of the two variables
- (x² - xy + y²) - a quadratic expression
This method allows you to break down the sum of cubes into simpler components, making it easier to work with in various mathematical contexts.
Approved Last Activity: 7 Months ago
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