Answer :
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.
