1. The like terms are $\frac{2}{3}x^2y$ and $-\frac{3}{7}x^2y$. Adding them: $\frac{2}{3}x^2y - \frac{3}{7}x^2y = (\frac{14}{21} - \frac{9}{21})x^2y = \frac{5}{21}x^2y$. The term $\frac{2}{7}x^2y^3$ is unlike and remains separate. Final answer: $\frac{5}{21}x^2y + \frac{2}{7}x^2y^3$.
2. All terms are unlike (different variables or combinations). They cannot be combined. Final answer: $8x - \frac{4}{3}x + \frac{2}{3}y + 3p$.
3. All terms are unlike (different variables or powers). They cannot be combined. Final answer: $1x^2 + 2y + 3z + 4x^2$.
4. The terms $x^2$ and $-3y^2$ are unlike (different variables). They cannot be combined. Final answer: $x^2 - 3y^2$.
5. The expression is $13 - y^2$. The numerical coefficient of the term $-y^2$ is $-1$.
6. Group and add like terms:
- x-terms: $12x - 25x + x = -12x$
- y-terms: $-25y + 12y + y = -12y$
- Constants: $12 + 1 - 25 = -12$
Final answer: $-12x - 12y - 12$.
7. In the expression $2x^2y - 15xy^2 + 7y^2$, the term containing $y^2$ is $7y^2$. Its coefficient is $7$.
8. Add $(3x + 11) + (-2x + y)$:
- Combine x-terms: $3x - 2x = x$
- Combine constants: $11$
- The y-term remains: $+ y$
Final answer: $x + y + 11$.
9. Subtract $(x + y)$ from $(\frac{3}{2}x - \frac{5}{2}y)$:
$(\frac{3}{2}x - \frac{5}{2}y) - (x + y) = \frac{3}{2}x - \frac{5}{2}y - x - y$
- Combine x-terms: $\frac{3}{2}x - x = \frac{1}{2}x$
- Combine y-terms: $-\frac{5}{2}y - y = -\frac{7}{2}y$
Final answer: $\frac{1}{2}x - \frac{7}{2}y$.
10. Substitute $x=2$ into $15x - 5x^2$:
$15(2) - 5(2)^2 = 30 - 5(4) = 30 - 20 = 10$.
Parent Tip: Review the logic above to help your child master the concept of 7th grade algebraic expressions worksheet.
