Question

date: ____________ bell: ____________ homework 7: combining like terms directions: simplify each expression by combining like terms. 1. $8y - 9y$ 2. $3x - 7x + 1$ 3. $8a - 6 + a - 1$ 4. $-2y + 14 - 9y + 5$ 5. $-x - 2 + 15x$ 6. $-7w - 5 - 7w + 9$ 7. $8d - 4 - d - 2$ 8. $40 - 9x + 4x + 5$ 9. $9a + 8 - 2a - 3 - 5a$ 10. $4xy - 6xy + 5y - 9x$ 11. $7x + 2y + 5 - 5x + 9y - 1$ 12. $-5f - 7g + f - 5g - 4 + f$ 13. $-6 + 3a - b - 4a + 4b + 5$ 14. $6n^{2}-2n - 3 + 5n^{2}-9n - 6$ 15. $8c^{2}-c + 3 + 2c^{2}-c + 2$ 16. $-12x^{2}y - 3x^{2}y$ 17. $6a^{2}b^{2}+3ab^{2}-a^{2}b^{2}-4ab^{2}$ 18. $19x^{2}y - 4xy^{2}+5xy^{2}-16x^{2}y$ 19. write the perimeter of the rectangle as a simplified expression. 20. write the perimeter of the triangle as a simplified expression.

Explanation:

Step1: Combine coefficients of like - terms

For \(8y - 9y\), since \(y\) is the like - term, we have \((8 - 9)y=-y\).

Step2: Combine \(x\) terms and constant

For \(3x - 7x+1\), combine \(x\) terms: \((3 - 7)x+1=-4x + 1\).

Step3: Combine \(a\) terms and constants

For \(8a-6 + a-1\), combine \(a\) terms \((8 + 1)a\) and constants \((-6-1)\), we get \(9a-7\).

Step4: Combine \(y\) terms and constants

For \(-2y + 14-9y + 5\), combine \(y\) terms \((-2-9)y\) and constants \((14 + 5)\), so \(-11y+19\).

Step5: Combine \(x\) terms

For \(-x-2 + 15x\), combine \(x\) terms \((-1 + 15)x-2 = 14x-2\).

Step6: Combine \(w\) terms and constants

For \(-7w-5-7w + 9\), combine \(w\) terms \((-7-7)w\) and constants \((-5 + 9)\), we have \(-14w + 4\).

Step7: Combine \(d\) terms and constants

For \(8d-4-d-2\), combine \(d\) terms \((8-1)d\) and constants \((-4-2)\), getting \(7d-6\).

Step8: Combine \(x\) terms and constants

For \(40-9x + 4x+5\), combine \(x\) terms \((-9 + 4)x\) and constants \((40 + 5)\), so \(-5x+45\).

Step9: Combine \(a\) terms and constants

For \(9a + 8-2a-3-5a\), combine \(a\) terms \((9-2-5)a\) and constants \((8-3)\), we obtain \(2a + 5\).

Step10: Combine \(xy\) terms

For \(4xy-6xy + 5y-9x\), combine \(xy\) terms \((4-6)xy+5y-9x=-2xy + 5y-9x\).

Step11: Combine \(x\) terms, \(y\) terms and constants

For \(7x + 2y+5-5x + 9y-1\), combine \(x\) terms \((7-5)x\), \(y\) terms \((2 + 9)y\) and constants \((5-1)\), getting \(2x+11y + 4\).

Step12: Combine \(f\) terms, \(g\) terms and constants

For \(-5f-7g + f-5g-4 + f\), combine \(f\) terms \((-5 + 1+1)f\) and \(g\) terms \((-7-5)g-4=-3f-12g-4\).

Step13: Combine \(a\) terms, \(b\) terms and constants

For \(-6 + 3a-b-4a + 4b+5\), combine \(a\) terms \((3-4)a\), \(b\) terms \((-1 + 4)b\) and constants \((-6 + 5)\), we have \(-a + 3b-1\).

Step14: Combine \(n^{2}\) terms and \(n\) terms and constants

For \(6n^{2}-2n-3 + 5n^{2}-9n-6\), combine \(n^{2}\) terms \((6 + 5)n^{2}\), \(n\) terms \((-2-9)n\) and constants \((-3-6)\), getting \(11n^{2}-11n-9\).

Step15: Combine \(c^{2}\) terms, \(c\) terms and constants

For \(8c^{2}-c + 3+2c^{2}-c + 2\), combine \(c^{2}\) terms \((8 + 2)c^{2}\), \(c\) terms \((-1-1)c\) and constants \((3 + 2)\), we obtain \(10c^{2}-2c + 5\).

Step16: Combine \(x^{2}y\) terms

For \(-12x^{2}y-3x^{2}y\), combine \(x^{2}y\) terms \((-12-3)x^{2}y=-15x^{2}y\).

Step17: Combine \(a^{2}b^{2}\) terms and \(ab^{2}\) terms

For \(6a^{2}b^{2}+3ab^{2}-a^{2}b^{2}-4ab^{2}\), combine \(a^{2}b^{2}\) terms \((6-1)a^{2}b^{2}\) and \(ab^{2}\) terms \((3-4)ab^{2}\), getting \(5a^{2}b^{2}-ab^{2}\).

Step18: Combine \(x^{2}y\) terms and \(xy^{2}\) terms

For \(19x^{2}y-4xy^{2}+5xy^{2}-16x^{2}y\), combine \(x^{2}y\) terms \((19-16)x^{2}y\) and \(xy^{2}\) terms \((-4 + 5)xy^{2}\), we have \(3x^{2}y+xy^{2}\).

Step19: Find perimeter of rectangle

The perimeter of a rectangle \(P = 2(l + w)\), where \(l=7x + 1\) and \(w=x-3\).
\[

$$\begin{align*} P&=2((7x + 1)+(x-3))\\ &=2(7x + 1+x-3)\\ &=2(8x-2)\\ &=16x-4 \end{align*}$$

\]

Step20: Find perimeter of triangle

The perimeter of a triangle \(P=(y - 4)+(3y + 5)+6y\).
\[

$$\begin{align*} P&=y-4+3y + 5+6y\\ &=(1 + 3+6)y+( - 4 + 5)\\ &=10y + 1 \end{align*}$$

\]

Answer:

1. \(-y\)
2. \(-4x + 1\)
3. \(9a-7\)
4. \(-11y+19\)
5. \(14x-2\)
6. \(-14w + 4\)
7. \(7d-6\)
8. \(-5x+45\)
9. \(2a + 5\)
10. \(-2xy + 5y-9x\)
11. \(2x+11y + 4\)
12. \(-3f-12g-4\)
13. \(-a + 3b-1\)
14. \(11n^{2}-11n-9\)
15. \(10c^{2}-2c + 5\)
16. \(-15x^{2}y\)
17. \(5a^{2}b^{2}-ab^{2}\)
18. \(3x^{2}y+xy^{2}\)
19. \(16x-4\)
20. \(10y + 1\)