The expression x²y + y2 is factored completely as y(x² + y).
The Breakdown
To factor the expression x²y + y2 completely, the common factor is y and we can apply Algebraic method.
Factor out y from both terms:
y(x² + y)
This is the least the sum can be factored using simple algebraic techniques. Therefore, the expression x²y + y2 is factored completely as y(x² + y).
Algebraic Method
The algebraic method refers to the process of rewriting an expression as a product of its factors. This involves identifying common factors, applying algebraic techniques such as grouping, factoring out common terms, or using specific factoring formulas.
The algebraic method can vary depending on the specific expression being factored. Some common techniques include factoring out the greatest common factor (GCF), factoring trinomials using methods like the quadratic formula or completing the square, or using special factoring formulas such as the difference of squares or the sum/difference of cubes.