Question

directions: simplify each expression by combining like terms. 1. 8y - 9y 3. 8a - 6 + a - 1 5. -x - 2 + 15x 7. 8d - 4 - d - 2 9. 9a + 8 - 2a - 3 - 5a 11. 7x + 2y + 5 - 5x + 9y - 1 13. -6 + 3a - b - 4a + 4b + 5 15. 8c² - c + 3 + 2c² - c + 2 17. 6a²b² + 3ab² - a²b² - 4ab² 19. write the perimeter of the rectangle as a simplified expression. x - 3 7x + 1

Explanation:

Step1: Combine like - terms in \(8y−9y\)

\(8y−9y=(8 - 9)y=-y\)

Step2: Combine like - terms in \(8a−6 + a−1\)

Group the \(a\) terms and the constant terms: \((8a + a)+(-6-1)=9a-7\)

Step3: Combine like - terms in \(-x−2 + 15x\)

\((-x + 15x)-2=14x-2\)

Step4: Combine like - terms in \(8d−4−d−2\)

Group the \(d\) terms and the constant terms: \((8d - d)+(-4-2)=7d-6\)

Step5: Combine like - terms in \(9a + 8−2a−3−5a\)

\((9a-2a-5a)+(8 - 3)=2a + 5\)

Step6: Combine like - terms in \(7x + 2y+5−5x + 9y−1\)

Group the \(x\) terms, \(y\) terms and constant terms: \((7x-5x)+(2y + 9y)+(5 - 1)=2x+11y + 4\)

Step7: Combine like - terms in \(-6 + 3a−b−4a + 4b+5\)

Group the \(a\) terms, \(b\) terms and constant terms: \((3a-4a)+(-b + 4b)+(-6 + 5)=-a + 3b-1\)

Step8: Combine like - terms in \(8c^{2}-c + 3+2c^{2}-c + 2\)

Group the \(c^{2}\) terms, \(c\) terms and constant terms: \((8c^{2}+2c^{2})+(-c - c)+(3 + 2)=10c^{2}-2c + 5\)

Step9: Combine like - terms in \(6a^{2}b^{2}+3ab^{2}-a^{2}b^{2}-4ab^{2}\)

Group the \(a^{2}b^{2}\) terms and \(ab^{2}\) terms: \((6a^{2}b^{2}-a^{2}b^{2})+(3ab^{2}-4ab^{2})=5a^{2}b^{2}-ab^{2}\)

Step10: Find the perimeter of the rectangle

The perimeter \(P\) of a rectangle with length \(l = 7x + 1\) and width \(w=x - 3\) is given by \(P = 2l+2w\).
\[

$$\begin{align*} P&=2(7x + 1)+2(x - 3)\\ &=14x+2 + 2x-6\\ &=(14x+2x)+(2 - 6)\\ &=16x-4 \end{align*}$$

\]

Answer:

1. \(-y\)
2. \(9a - 7\)
3. \(14x-2\)
4. \(7d-6\)
5. \(2a + 5\)
6. \(2x+11y + 4\)
7. \(-a + 3b-1\)
8. \(10c^{2}-2c + 5\)
9. \(5a^{2}b^{2}-ab^{2}\)
10. \(16x-4\)