Math  /  Algebra

QuestionQuestion Wate
Factor the expression completely. x2y3+y4x^{2} y^{3}+y^{4}
Answer

Studdy Solution

STEP 1

1. We are asked to factor the expression completely.
2. The expression is a polynomial with two terms.
3. Factoring involves finding the greatest common factor and using algebraic identities if applicable.

STEP 2

1. Identify the greatest common factor (GCF) of the terms in the expression.
2. Factor out the GCF from the expression.
3. Check if the resulting expression can be factored further.

STEP 3

Identify the greatest common factor (GCF) of the terms x2y3x^{2} y^{3} and y4y^{4}.
The GCF is y3y^{3} because it is the highest power of yy common to both terms.

STEP 4

Factor out the GCF y3y^{3} from the expression:
x2y3+y4=y3(x2+y) x^{2} y^{3} + y^{4} = y^{3}(x^{2} + y)

STEP 5

Check if the expression inside the parentheses, x2+yx^{2} + y, can be factored further.
Since x2+yx^{2} + y does not have any common factors and is not a recognizable algebraic identity, it cannot be factored further.
The completely factored expression is:
y3(x2+y) \boxed{y^{3}(x^{2} + y)}

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