1. $\frac{2}{3}x^2y + \frac{-3}{7}x^2y = \left(\frac{2}{3} - \frac{3}{7}\right)x^2y = \left(\frac{14 - 9}{21}\right)x^2y = \frac{5}{21}x^2y$. The term $\frac{2}{7}x^2y^3$ is unlike and remains as is. Final answer: $\frac{5}{21}x^2y + \frac{2}{7}x^2y^3$.
2. $8x + \frac{-4}{3}x + \frac{2}{3}y + 3p = \left(8 - \frac{4}{3}\right)x + \frac{2}{3}y + 3p = \frac{20}{3}x + \frac{2}{3}y + 3p$.
3. $1x^2 + 2y + 3z + 4x^2 = (1 + 4)x^2 + 2y + 3z = 5x^2 + 2y + 3z$.
4. $x^2 + (-3y^2) = x^2 - 3y^2$.
5. The numerical coefficient of $y^2$ in $13 - y^2$ is $-1$.
6. Group like terms: $(12x - 25x + x) + (-25y + 12y + y) + (12 + 1 - 25) = (-12x) + (-12y) + (-12) = -12x - 12y - 12$.
7. In $2x^2y - 15xy^2 + 7y^2$, the coefficient of $y^2$ is $7$ (from the term $7y^2$).
8. $(3x + 11) + (-2x + y) = (3x - 2x) + y + 11 = x + y + 11$.
9. $\left(\frac{3}{2}x - \frac{5}{2}y\right) - (x + y) = \frac{3}{2}x - \frac{5}{2}y - x - y = \left(\frac{3}{2} - 1\right)x + \left(-\frac{5}{2} - 1\right)y = \frac{1}{2}x - \frac{7}{2}y$.
10. Substitute $x = 2$: $15(2) - 5(2)^2 = 30 - 5(4) = 30 - 20 = 10$.
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions worksheets.
