Question

name date practice combining like terms which terms are like terms? (not all terms will be used) circle all terms that can be combined with 3a. draw a square around all terms that can be combined with 4b. underline all terms that can be combined with a². draw an x through all terms that can be combined with 5. 1. 14a 2. 5ab 3. 3b 4. 3a² 5. 4b² 6. 17 7. 100 8. 14ab 9. 5a³ 10. 4a 11. 16b 12. 73a² simplify the following expressions by combining like terms. show all work on a separate sheet of paper and box your answer. 13. 4x - 6x 14. 7y + 5y - 5y 15. 4r + 4y - 8 16. 3m + 4n - 6n 17. 4g + 6g - 3g 18. 15f - 5 + 2f 19. 13x - 7y + 4x 20. 5x² - 4x + 9x² 21. 4b + 7a - 8 22. 13r + 5s - 2r 23. a + a + 3b + b 24. 3y - 4y² + 3y 25. (3a - b) + 2a 26. 2w + 4w² - 5w³ 27. c³ + 4c - 4c³ 28. a - 3b + 5c + 4a 29. 2x + 7x - 6x + 8 30. 11q + 5p - 9q + 7p 31. 3mn + 4m - 2mn 32. 0t - 9t + 6u + 4u⁵ 33. 11d + 5f - 21d + 5 - 8 34. 12 + 9x - 6x - 19 35. y² + 3y² - 6y + 4y² 36. 2 - 5t + 8 + 5t - 8 when part of an expression is over or under a division bar, you must act as if that part of the expression is inside of parenthesis. use pemdas to decide if you can simplify the expression any further. (think: did you get a fraction that you can simplify?) 37. \\( \frac{14r + 12s}{4s - 10s} \\) 38. \\( \frac{3x²}{12 - 14x²} \\) 39. \\( \frac{2 - 5t}{2 + 5t - 4t} \\) 40. \\( \frac{2x - 6y + 4x}{3y - 8 + y} \\) 41. \\( \frac{11d + 9d}{8d - 3d} \\) 42. \\( \frac{12x - 7x}{5x} \\) bonus: simplify the expression below by combining like terms. 4z + x - 5x + 7y - 3x + 5y² - 3z + 16z + 14x - 5

Explanation:

Step1: Combine like terms for \(4x - 6x\)

Like terms are terms with the same variable raised to the same power. For \(4x-6x\), we use the distributive property \(ax - bx=(a - b)x\). Here \(a = 4\) and \(b=6\), so \(4x-6x=(4 - 6)x=-2x\)

Step2: Combine like terms for \(7y + 5y-5y\)

First, combine \(7y+5y=(7 + 5)y = 12y\), then \(12y-5y=(12 - 5)y = 7y\)

Step3: Combine like terms for \(4r + 4y-8\)

There are no like - terms ( \(4r\), \(4y\), and \(-8\) have different variables or are a constant), so it remains \(4r + 4y-8\)

Step4: Combine like terms for \(3m + 4n-6n\)

Combine \(4n-6n=(4 - 6)n=-2n\), so the expression is \(3m-2n\)

Step5: Combine like terms for \(4g + 6g-3g\)

Using the distributive property \(ag+bg - cg=(a + b - c)g\), where \(a = 4\), \(b = 6\), \(c = 3\). Then \((4 + 6-3)g=7g\)

Step6: Combine like terms for \(15f-5 + 2f\)

Combine \(15f+2f=(15 + 2)f = 17f\), so the expression is \(17f-5\)

Step7: Combine like terms for \(13x-7y + 4x\)

Combine \(13x+4x=(13 + 4)x = 17x\), so the expression is \(17x-7y\)

Step8: Combine like terms for \(5x^{2}-4x + 9x^{2}\)

Combine \(5x^{2}+9x^{2}=(5 + 9)x^{2}=14x^{2}\), so the expression is \(14x^{2}-4x\)

Step9: Combine like terms for \(4b + 7a-8\)

There are no like - terms ( \(4b\), \(7a\), and \(-8\) have different variables or are a constant), so it remains \(4b + 7a-8\)

Step10: Combine like terms for \(13r + 5s-2r\)

Combine \(13r-2r=(13 - 2)r = 11r\), so the expression is \(11r + 5s\)

Step11: Combine like terms for \(a + a+3b + b\)

Combine \(a + a=(1 + 1)a = 2a\) and \(3b + b=(3 + 1)b = 4b\), so the expression is \(2a + 4b\)

Step12: Combine like terms for \(3y-4y^{2}+3y\)

Combine \(3y+3y=(3 + 3)y = 6y\), so the expression is \(-4y^{2}+6y\)

Step13: Combine like terms for \((3a - b)+2a\)

First, remove the parentheses (since there is a \(+\) sign in front of the parentheses). Then \(3a - b+2a\). Combine \(3a+2a=(3 + 2)a = 5a\), so the expression is \(5a - b\)

Step14: Combine like terms for \(2w + 4w^{2}-5w^{3}\)

There are no like - terms ( \(2w\), \(4w^{2}\), and \(-5w^{3}\) have different powers of \(w\)), so it remains \(2w + 4w^{2}-5w^{3}\)

Step15: Combine like terms for \(c^{3}+4c-4c^{3}\)

Combine \(c^{3}-4c^{3}=(1 - 4)c^{3}=-3c^{3}\), so the expression is \(-3c^{3}+4c\)

Step16: Combine like terms for \(a-3b + 5c+4a\)

Combine \(a + 4a=(1 + 4)a = 5a\), so the expression is \(5a-3b + 5c\)

Step17: Combine like terms for \(2x + 7x-6x + 8\)

Combine \(2x+7x-6x=(2 + 7-6)x = 3x\), so the expression is \(3x + 8\)

Step18: Combine like terms for \(11q + 5p-9q+7p\)

Combine \(11q-9q=(11 - 9)q = 2q\) and \(5p+7p=(5 + 7)p = 12p\), so the expression is \(2q + 12p\)

Step19: Combine like terms for \(3mn + 4m-2mn\)

Combine \(3mn-2mn=(3 - 2)mn = mn\), so the expression is \(mn + 4m\)

Step20: Combine like terms for \(0t-9t + 6u+4u^{5}\)

Combine \(0t-9t=(0 - 9)t=-9t\), so the expression is \(-9t + 6u+4u^{5}\)

Step21: Combine like terms for \(11d + 5f-21d+5 - 8\)

Combine \(11d-21d=(11 - 21)d=-10d\) and \(5 - 8=-3\), so the expression is \(-10d+5f - 3\)

Step22: Combine like terms for \(12 + 9x-6x-19\)

Combine \(9x-6x=(9 - 6)x = 3x\) and \(12-19=-7\), so the expression is \(3x-7\)

Step23: Combine like terms for \(y^{2}+3y^{2}-6y + 4y^{2}\)

Combine \(y^{2}+3y^{2}+4y^{2}=(1 + 3+4)y^{2}=8y^{2}\), so the expression is \(8y^{2}-6y\)

Step24: Combine like terms for \(2-5t + 8+5t-8\)

Combine \(-5t+5t=( - 5 + 5)t = 0\) and \(2 + 8-8=2\), so the expression is \(2\)

Step25: Simplify \(\frac{14r + 12s}{4s-10s}\)

First, simplify the denominator \(4s-10s=(4 - 10)s=-6s\). The numerator \(14r + 12s\) has no like - terms with the denominator (since \(r\) and \(s\) are different variables). So the expression is \(\frac{14r + 12s}{-6s}=-\frac{14r}{6s}-\frac{12s}{6s}=-\frac{7r}{3s}-2\)

Step26: Simplify \(\frac{3x^{2}}{12-14x^{2}}\)

There are no like - terms to combine in the numerator and denominator ( \(3x^{2}\) and \(12-14x^{2}\) have different structures), so it remains \(\frac{3x^{2}}{12-14x^{2}}\)

Step27: Simplify \(\frac{2-5t}{2 + 5t-4t}\)

Simplify the denominator \(2+5t-4t=2+(5 - 4)t=2 + t\). The numerator \(2-5t\) has no like - terms with the denominator (since of the different variable terms). So the expression is \(\frac{2-5t}{2 + t}\)

Step28: Simplify \(\frac{2x-6y + 4x}{3y-8 + y}\)

Simplify the numerator \(2x+4x=(2 + 4)x = 6x\), so the numerator is \(6x-6y\). Simplify the denominator \(3y + y=(3 + 1)y = 4y\), so the denominator is \(4y-8\). Then \(\frac{6x-6y}{4y-8}=\frac{6(x - y)}{4(y - 2)}=\frac{3(x - y)}{2(y - 2)}\)

Step29: Simplify \(\frac{11d + 9d}{8d-3d}\)

Simplify the numerator \(11d+9d=(11 + 9)d = 20d\). Simplify the denominator \(8d-3d=(8 - 3)d = 5d\). Then \(\frac{20d}{5d}=4\)

Step30: Simplify \(\frac{12x-7x}{5x}\)

Simplify the numerator \(12x-7x=(12 - 7)x = 5x\). Then \(\frac{5x}{5x}=1\)

Step31: Simplify \(4z+x-5x + 7y-3x+5y^{2}-3z + 16z+14x-5\)

Combine \(z\) terms: \(4z-3z + 16z=(4-3 + 16)z = 17z\)
Combine \(x\) terms: \(x-5x-3x+14x=(1-5-3 + 14)x = 7x\)
The \(y\) term is \(7y\) and the \(y^{2}\) term is \(5y^{2}\) and the constant is \(-5\)
So the expression is \(17z+7x + 7y+5y^{2}-5\)

Answer:

1. \(-2x\)
2. \(7y\)
3. \(4r + 4y-8\)
4. \(3m-2n\)
5. \(7g\)
6. \(17f-5\)
7. \(17x-7y\)
8. \(14x^{2}-4x\)
9. \(4b + 7a-8\)
10. \(11r + 5s\)
11. \(2a + 4b\)
12. \(-4y^{2}+6y\)
13. \(5a - b\)
14. \(2w + 4w^{2}-5w^{3}\)
15. \(-3c^{3}+4c\)
16. \(5a-3b + 5c\)
17. \(3x + 8\)
18. \(2q + 12p\)
19. \(mn + 4m\)
20. \(-9t + 6u+4u^{5}\)
21. \(-10d+5f - 3\)
22. \(3x-7\)
23. \(8y^{2}-6y\)
24. \(2\)
25. \(-\frac{7r}{3s}-2\)
26. \(\frac{3x^{2}}{12-14x^{2}}\)
27. \(\frac{2-5t}{2 + t}\)
28. \(\frac{3(x - y)}{2(y - 2)}\)
29. \(4\)
30. \(1\)

Bonus. \(17z+7x + 7y+5y^{2}-5\)