Answer:
Explanation:
The given expression is (2x² + 3y²z²) - (x² - y² - 2²) + (4x²-3y²). To simplify this expression, we need to apply the rules of algebraic operations.
Step 1: Simplify the terms within each set of parentheses.
Within the first set of parentheses, we have 2x² + 3y²z². Since there are no like terms to combine, this term remains as it is.
Within the second set of parentheses, we have x² - y² - 2². Here, we can simplify by expanding the square term: 2² = 4. Thus, the term becomes x² - y² - 4.
Within the third set of parentheses, we have 4x² - 3y². Again, there are no like terms to combine, so this term remains unchanged.
Step 2: Apply the subtraction operation between the sets of parentheses.
Now, we can rewrite the expression as follows:
(2x² + 3y²z²) - (x² - y² - 4) + (4x² - 3y²).
Step 3: Distribute the negative sign to each term within the second set of parentheses.
This step involves changing the signs of each term within the second set of parentheses:
(2x² + 3y²z²) + (-x² + y² + 4) + (4x² - 3y²).
Step 4: Combine like terms.
Now, we can combine like terms in order to simplify further:
2x² + (-x²) + 4x² = x² + 4x² = 5x²
3y²z² + y² = (3z² + 1)y²
4 + (-3y²) = 4 - 3y²
The final simplified expression is:
5x² + (3z² + 1)y² + 4 - 3y².