Question

name date practice combining like terms which terms are like terms? (not all terms will be used.) circle all terms that draw a square around underline all terms draw an x through all can be combined with all terms that can be that can be combined terms that can be 3a. combined with 4b. with ( a^{2} ). combined with 5. 1. 14a 2. 5ab 3. 3b 4. ( 3a^{2} ) 5. ( 4b^{2} ) 6. 17 7. 100 8. 14ab 9. ( 5a^{3} ) 10. 4a 11. 16b 12. ( 73a^{2} ) 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. ( 5x^{2} - 4x + 9x^{2} ) 21. ( 4b + 7a - 8 ) 22. ( 13r + 5s - 2r ) 23. ( a + a + 3b + b ) 24. ( 3y - 4y^{2} + 3y ) 25. ( (3a - b) + 2a ) 26. ( 2w + 4w^{2} - 5w^{3} ) 27. ( c^{3} + 4c - 4c^{3} ) 28. ( a - 3b + 5c + 4a ) 29. ( 2x + 7x - 6x + 8 ) 30. ( 11q + 5p - 9q + 7p ) 31. ( 3mn + 4m - 2mn ) 32. ( 0t - 9t + 6u + 4u^{5} ) 33. ( 11d + 5f - 21d + 5 - 8 ) 34. ( 12 + 9x - 6x - 19 ) 35. ( y^{2} + 3y^{2} - 6y + 4y^{2} ) 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{3y^{2}}{12 - 14x^{2}} ) 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}{6x} ) bonus: simplify the expression below by combining like terms. ( 4z + x - 5x + 7y - 3x + 6y^{2} - 3x + 16z + 14x - 5 )

Explanation:

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

Like terms have the same variable part. Here, \(4x\) and \(6x\) are like terms. Using the rule \(ax+bx=(a + b)x\), we have \(4x-6x=(4 - 6)x\)
\(4x-6x=-2x\)

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

First, combine \(7y\) and \(5y\): \(7y + 5y=(7 + 5)y = 12y\). Then subtract \(5y\) from the result. So \(12y-5y=(12 - 5)y\)
\(7y + 5y-5y = 7y\)

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

There are no like - terms among \(4r\), \(4y\), and \(-8\) (since \(r\) and \(y\) are different variables). So the expression remains as \(4r + 4y-8\)

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

The like terms are \(4n\) and \(-6n\). Using \(an+bn=(a + b)n\), we get \(4n-6n=(4 - 6)n=-2n\). So the expression is \(3m-2n\)

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

Combine \(4g\), \(6g\), and \(-3g\). Using \(ag+bg+cg=(a + b + c)g\), we have \((4 + 6-3)g\)
\(4g+6g - 3g=7g\)

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

Combine \(15f\) and \(2f\) (like terms with variable \(f\)). Using \(af+bf=(a + b)f\), we get \((15 + 2)f-5\)
\(15f-5 + 2f=17f-5\)

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

Combine \(13x\) and \(4x\) (like terms with variable \(x\)). Using \(ax+bx=(a + b)x\), we have \((13 + 4)x-7y\)
\(13x-7y + 4x=17x-7y\)

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

Combine \(5x^{2}\) and \(9x^{2}\) (like terms with variable \(x^{2}\)). Using \(ax^{2}+bx^{2}=(a + b)x^{2}\), we get \((5 + 9)x^{2}-4x\)
\(5x^{2}-4x + 9x^{2}=14x^{2}-4x\)

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

There are no like - terms among \(4b\), \(7a\), and \(-8\) (since \(a\) and \(b\) are different variables). So the expression remains as \(4b + 7a-8\)

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

Combine \(13r\) and \(-2r\) (like terms with variable \(r\)). Using \(ar+br=(a + b)r\), we have \((13-2)r + 5s\)
\(13r + 5s-2r=11r + 5s\)

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

Combine \(a\) and \(a\) (like terms with variable \(a\)) and \(3b\) and \(b\) (like terms with variable \(b\)). Using \(ax+bx=(a + b)x\), we get \((1 + 1)a+(3 + 1)b\)
\(a + a+3b + b=2a + 4b\)

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

Combine \(3y\) and \(3y\) (like terms with variable \(y\)). Using \(ay+by=(a + b)y\), we get \((3 + 3)y-4y^{2}\)
\(3y-4y^{2}+3y=6y-4y^{2}\)

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

First, remove the parentheses: \(3a - b+2a\). Then combine \(3a\) and \(2a\) (like terms with variable \(a\)). Using \(ax+bx=(a + b)x\), we have \((3 + 2)a - b\)
\((3a - b)+2a=5a - b\)

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

There are no like - terms among \(2w\), \(4w^{2}\), and \(-5w^{3}\) (since the exponents of \(w\) are different). So the expression remains as \(2w + 4w^{2}-5w^{3}\)

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

Combine \(c^{3}\) and \(-4c^{3}\) (like terms with variable \(c^{3}\)). Using \(ac^{3}+bc^{3}=(a + b)c^{3}\), we get \((1-4)c^{3}+4c\)
\(c^{3}+4c-4c^{3}=-3c^{3}+4c\)

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

Combine \(a\) and \(4a\) (like terms with variable \(a\)). Using \(ax+bx=(a + b)x\), we have \((1 + 4)a-3b + 5c\)
\(a-3b + 5c+4a=5a-3b + 5c\)

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

Combine \(2x\), \(7x\), and \(-6x\) (like terms with variable \(x\)). Using \(ax+bx+cx=(a + b + c)x\), we get \((2 + 7-6)x+8\)
\(2x+7x-6x + 8=3x+8\)

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

Combine \(11q\) and \(-9q\) (like terms with variable \(q\)) and \(5p\) and \(7p\) (like terms with variable \(p\)). Using \(ax+bx=(a + b)x\), we have \((11-9)q+(5 + 7)p\)
\(11q + 5p-9q + 7p=2q + 12p\)

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

Combine \(3mn\) and \(-2mn\) (like terms with variable \(mn\)). Using \(amn+bmn=(a + b)mn\), we get \((3-2)mn+4m\)
\(3mn+4m-2mn=mn + 4m\)

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

Combine \(0t\) and \(-9t\) (like terms with variable \(t\)). Using \(at+bt=(a + b)t\), we get \((0-9)t+6u + 4u^{5}\)
\(0t-9t+6u + 4u^{5}=-9t+6u + 4u^{5}\)

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

Combine \(11d\) and \(-21d\) (like terms with variable \(d\)) and \(5\) and \(-8\) (constant terms). Using \(ad+bd=(a + b)d\) and \(a + b=(a + b)\), we get \((11-21)d+5f+(5 - 8)\)
\(11d+5f-21d + 5-8=-10d+5f-3\)

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

Combine \(9x\) and \(-6x\) (like terms with variable \(x\)) and \(12\) and \(-19\) (constant terms). Using \(ax+bx=(a + b)x\) and \(a + b=(a + b)\), we get \((9-6)x+(12-19)\)
\(12 + 9x-6x-19=3x-7\)

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

Combine \(y^{2}\), \(3y^{2}\), and \(4y^{2}\) (like terms with variable \(y^{2}\)). Using \(ay^{2}+by^{2}+cy^{2}=(a + b + c)y^{2}\), we get \((1 + 3+4)y^{2}-6y\)
\(y^{2}+3y^{2}-6y + 4y^{2}=8y^{2}-6y\)

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

Combine \(-5t\) and \(5t\) (like terms with variable \(t\)) and \(2\), \(8\), and \(-8\) (constant terms). Using \(at+bt=(a + b)t\) and \(a + b + c=(a + b + c)\), we get \((-5 + 5)t+(2 + 8-8)\)
\(2-5t+8 + 5t-8=2\)

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. \(6y-4y^{2}\)
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. \(2\)