For each of the following , simplify by combining like terms :
4x^3y+5x(6xy-7y^2) - 8y(9x^2-10xy) - 11xy^2
first expand:
4x^3y+30x^2y-35xy^2-72x^2y+80xy^2-11xy^2
then combine:
4x^3y-42x^2y-34xy^2
To simplify the given expression by combining like terms, we need to combine the terms that have the same variables and exponents.
Let's break down the given expression step by step and combine like terms:
1. 4x^3y: This term has only one similar term, which is 5x(6xy-7y^2). We can't combine them yet, so let's move on.
2. Next, we have 5x(6xy-7y^2). To combine like terms here, distribute the '5x' to both terms inside the parentheses:
5x * 6xy = 30x^2y
5x * -7y^2 = -35xy^2
After combining these terms, we get:
4x^3y + 30x^2y - 35xy^2
3. After that, we have - 8y(9x^2-10xy). Again, distribute the '-8y' to both terms inside the parentheses:
-8y * 9x^2 = -72x^2y
-8y * -10xy = 80xy^2
After combining these terms, we get:
4x^3y + 30x^2y - 35xy^2 - 72x^2y + 80xy^2
4. Finally, we have - 11xy^2. This term doesn't have any other similar terms, so it remains as it is.
By combining the like terms, the simplified form of the given expression is:
4x^3y + 30x^2y - 72x^2y - 35xy^2 + 80xy^2 - 11xy^2
To further simplify, let's combine the like terms:
4x^3y + (30x^2y - 72x^2y) + (-35xy^2 + 80xy^2 - 11xy^2)
Simplifying the combined like terms, we get:
4x^3y - 42x^2y + 34xy^2
Therefore, the simplified form of the given expression by combining like terms is:
4x^3y - 42x^2y + 34xy^2