Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Sure! Let's break down the expression [tex]\( x y(x^2 + x - 3) \)[/tex] step by step.
### Step 1: Understand the Expression
The given expression is [tex]\( x y(x^2 + x - 3) \)[/tex]. This is a product of [tex]\( xy \)[/tex] and the polynomial [tex]\( x^2 + x - 3 \)[/tex].
### Step 2: Distribute [tex]\( x \)[/tex] over the Polynomial
First, we can distribute [tex]\( x \)[/tex] in [tex]\( xy(x^2 + x - 3) \)[/tex]:
[tex]\[ x \cdot (x^2 + x - 3) = x^3 + x^2 x - 3x \][/tex]
### Step 3: Combine with [tex]\( y \)[/tex]
Now multiply the entire expression by [tex]\( y \)[/tex]:
[tex]\[ y \cdot (x^3 + x^2 + x - 3x) = y x^3 + y x^2 + y x - 3 y x \][/tex]
### Step 4: Combine like terms
Rewriting the expression for better clarity:
[tex]\[ x y(x^3 + x^2 + x - 3) \][/tex]
In this, we see how each term [tex]\( x \)[/tex] in [tex]\( x^2 + x - 3 \)[/tex] has been multiplied by both [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Final Expression
Thus, the expression [tex]\( x y(x^2 + x - 3) \)[/tex] simplifies directly to the expanded form:
[tex]\[ x y(x^2 + x - 3) \][/tex]
So, the final simplified form of [tex]\( x y (x^2 + x - 3) \)[/tex] is indeed:
[tex]\[ x y(x^2 + x - 3) \][/tex]
This reproduces the final result clearly and steps you through the expression manipulation.
### Step 1: Understand the Expression
The given expression is [tex]\( x y(x^2 + x - 3) \)[/tex]. This is a product of [tex]\( xy \)[/tex] and the polynomial [tex]\( x^2 + x - 3 \)[/tex].
### Step 2: Distribute [tex]\( x \)[/tex] over the Polynomial
First, we can distribute [tex]\( x \)[/tex] in [tex]\( xy(x^2 + x - 3) \)[/tex]:
[tex]\[ x \cdot (x^2 + x - 3) = x^3 + x^2 x - 3x \][/tex]
### Step 3: Combine with [tex]\( y \)[/tex]
Now multiply the entire expression by [tex]\( y \)[/tex]:
[tex]\[ y \cdot (x^3 + x^2 + x - 3x) = y x^3 + y x^2 + y x - 3 y x \][/tex]
### Step 4: Combine like terms
Rewriting the expression for better clarity:
[tex]\[ x y(x^3 + x^2 + x - 3) \][/tex]
In this, we see how each term [tex]\( x \)[/tex] in [tex]\( x^2 + x - 3 \)[/tex] has been multiplied by both [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Final Expression
Thus, the expression [tex]\( x y(x^2 + x - 3) \)[/tex] simplifies directly to the expanded form:
[tex]\[ x y(x^2 + x - 3) \][/tex]
So, the final simplified form of [tex]\( x y (x^2 + x - 3) \)[/tex] is indeed:
[tex]\[ x y(x^2 + x - 3) \][/tex]
This reproduces the final result clearly and steps you through the expression manipulation.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.