Questionhe expression completely. $x y+x^{4} y^{5}$

Studdy Solution

STEP 1

1. The expression given is $xy + x^4y^5$ .
2. We are required to factor the expression completely.
3. Factoring involves finding common factors and using algebraic identities if applicable.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Simplify the expression by factoring out the GCF.

STEP 3

Identify the greatest common factor (GCF) in the terms $xy$ and $x^4y^5$ .
- The GCF of $x$ and $x^4$ is $x$ . - The GCF of $y$ and $y^5$ is $y$ .
Thus, the GCF of the entire expression is $xy$ .

STEP 4

Factor out the GCF $xy$ from the expression:
$xy + x^4y^5 = xy(1 + x^3y^4)$
This expression is now completely factored.
The completely factored expression is:
$\boxed{xy(1 + x^3y^4)}$

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