Answer :
Sure, let's solve the expression step-by-step.
Given the mathematical expression:
[tex]\[ x^3 y + x^2 y - 3 x y \][/tex]
### Step 1: Identify Common Factors
First, observe that each term in the expression contains both [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. We can factor out [tex]\(xy\)[/tex] from the expression.
### Step 2: Factor [tex]\(xy\)[/tex] out of the Expression
When we factor [tex]\(xy\)[/tex] out of each term, we have:
[tex]\[ x^3 y + x^2 y - 3 x y = xy (x^2 + x - 3) \][/tex]
### Step 3: Validate Factoring
To ensure that factoring is correct, we can distribute [tex]\(xy\)[/tex] back into the expression:
[tex]\[ xy (x^2 + x - 3) = x^3 y + x^2 y - 3 x y \][/tex]
Thus, we see that our factoring is correct.
### Conclusion
The simplified form of the given expression after factoring is:
[tex]\[ xy (x^2 + x - 3) \][/tex]
So, the given expression [tex]\( x^3 y + x^2 y - 3 x y \)[/tex] can be factored as [tex]\( xy (x^2 + x - 3) \)[/tex].
Given the mathematical expression:
[tex]\[ x^3 y + x^2 y - 3 x y \][/tex]
### Step 1: Identify Common Factors
First, observe that each term in the expression contains both [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. We can factor out [tex]\(xy\)[/tex] from the expression.
### Step 2: Factor [tex]\(xy\)[/tex] out of the Expression
When we factor [tex]\(xy\)[/tex] out of each term, we have:
[tex]\[ x^3 y + x^2 y - 3 x y = xy (x^2 + x - 3) \][/tex]
### Step 3: Validate Factoring
To ensure that factoring is correct, we can distribute [tex]\(xy\)[/tex] back into the expression:
[tex]\[ xy (x^2 + x - 3) = x^3 y + x^2 y - 3 x y \][/tex]
Thus, we see that our factoring is correct.
### Conclusion
The simplified form of the given expression after factoring is:
[tex]\[ xy (x^2 + x - 3) \][/tex]
So, the given expression [tex]\( x^3 y + x^2 y - 3 x y \)[/tex] can be factored as [tex]\( xy (x^2 + x - 3) \)[/tex].
