To simplify the expression [tex]\(\left(6 x^4 y^2-3 x y^3-4 x y\right)+\left(4 x^4 y^2-x y^3+4 x y\right)\)[/tex], let's go through it step-by-step.
1. Write down the expression:
[tex]\[
(6x^4y^2 - 3xy^3 - 4xy) + (4x^4y^2 - xy^3 + 4xy)
\][/tex]
2. Combine like terms:
- Combine the [tex]\(x^4y^2\)[/tex] terms:
[tex]\[
6x^4y^2 + 4x^4y^2 = 10x^4y^2
\][/tex]
- Combine the [tex]\(xy^3\)[/tex] terms:
[tex]\[
-3xy^3 - xy^3 = -4xy^3
\][/tex]
- Combine the [tex]\(xy\)[/tex] terms:
[tex]\[
-4xy + 4xy = 0
\][/tex]
So, summing up the combined terms, we get:
[tex]\[
10x^4y^2 - 4xy^3
\][/tex]
3. Output the result:
The combined and simplified expression is:
[tex]\[
10x^4y^2 - 4xy^3
\][/tex]
4. Factor the simplified expression (if possible):
To factor the expression [tex]\(10x^4y^2 - 4xy^3\)[/tex], we look for common factors:
- Both terms contain [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- We can factor out the greatest common divisor (GCD), which is [tex]\(2xy^2\)[/tex].
The factored form is:
[tex]\[
10x^4y^2 - 4xy^3 = 2xy^2(5x^3 - 2y)
\][/tex]
Therefore, the simplified expression is:
[tex]\[
10x^4y^2 - 4xy^3
\][/tex]
The factored form is:
[tex]\[
2xy^2(5x^3 - 2y)
\][/tex]
