Find: (4*x*2*y*3 + 2*xy*2 – 2*y*) – (–7*x*2*y*3 + 6*xy*2 – 2*y*)

Place the correct coefficients in the difference.

*x*2*y*3 + *xy*2 + *y*

To solve \((4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y)\), we will first distribute the negative sign through the second set of parentheses, and then combine like terms.

First, distribute the negative sign:
\[4x^2y^3 + 2xy^2 - 2y - (-7x^2y^3 + 6xy^2 - 2y)\]
\[= 4x^2y^3 + 2xy^2 - 2y + 7x^2y^3 - 6xy^2 + 2y\]

Now, combine like terms:
1. Combine the \(x^2y^3\) terms:
\[4x^2y^3 + 7x^2y^3 = 11x^2y^3\]

2. Combine the \(xy^2\) terms:
\[2xy^2 - 6xy^2 = -4xy^2\]

3. Combine the \(y\) terms:
\[-2y + 2y = 0\]

Thus, the resulting expression is:
\[11x^2y^3 - 4xy^2\]

The coefficients for \(x^2y^3\), \(xy^2\), and \(y\) are \(11\), \(-4\), and \(0\) respectively.

If you have any questions or need further details, please let me know.

Here are 5 more questions you might find interesting:

1. Simplify the expression \((3a^2b + 2ab^2 - 4b) - (5a^2b - ab^2 + 3b)\).
2. Factor the polynomial \(x^3 - 3x^2 + 2x\).
3. Solve the quadratic equation \(2x^2 - 5x + 3 = 0\).
4. Find the derivative of \(f(x) = x^4 - 2x^3 + x - 5\).
5. Evaluate the integral \(\int (3x^2 - 2x + 1) dx\).

**Tip:** When combining like terms, always ensure that you correctly align the terms with the same variables and powers to avoid mistakes.

Learn how to combine and simplify polynomials by solving (4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y). This problem involves polynomials with multiple terms and includes steps such as distribution and combining like terms. Suitable for students in Grades 7-9 studying algebra.

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