Simplify Algebraic Expression Involving Squared Terms

Math Problem Statement

this ^ mean squared

Thank you for the clarification! Let's rework the expression considering that ^ means "squared."

Given expression:

$-y^2 - z^2 - xy + 1 + 3xy + 2y - 3x^2 - 5 + xy + 3xy - z^2$

&(-y^2) &\text{(term with } y^2) \\ &(-z^2 - z^2) &\text{(terms with } z^2) \\ &(-xy + 3xy + xy + 3xy) &\text{(terms with } xy) \\ &(-3x^2) &\text{(term with } x^2) \\ &(2y) &\text{(term with } y) \\ &(1 - 5) &\text{(constant terms)} \end{aligned}$$ 2. **Combine the terms:** $$y^2: -y^2 \quad \text{(no other } y^2 \text{ terms to combine with)}$$ $$z^2: -z^2 - z^2 = -2z^2$$ $$xy: -xy + 3xy + xy + 3xy = 6xy$$ $$x^2: -3x^2$$ $$y: 2y \quad \text{(no other } y \text{ terms to combine with)}$$ $$\text{Constants: } 1 - 5 = -4$$ 3. **Combine all the simplified terms:** $$-y^2 - 2z^2 + 6xy - 3x^2 + 2y - 4$$ So, the simplified expression is: $$-y^2 - 2z^2 + 6xy - 3x^2 + 2y - 4$$ Would you like further explanation on any steps? Here are some related questions: 1. How do exponents affect the grouping of like terms? 2. Why is it important to combine like terms in algebra? 3. Can you give an example of how exponents change when terms are combined? 4. What does it mean when a term has a negative coefficient? 5. How do you handle terms with different variables when simplifying? **Tip:** Always pay attention to the signs and exponents when combining terms to ensure accuracy!

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Algebra
Combining Like Terms

Grades 7-9

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