Math Problem Statement

Simplify the following algebraic expressions: a. 5p + 6p - 3p b. 8m - 3m - 2m + 7m c. 8x - 5x + 7x d. 4xy + 6xy - 3xy - 2xy e. 12y - 4y + 5y f. 8k + 4k + 2k - 5k g. 8xy + 2xy + 5xy h. 9a + 2a + 3a - 7a i. 6m - 3m + 10m j. 11p + 5p - 7p k. 5a + 7a + 3a + 6a l. 6ab - 3ab - ab + 2ab

Solution

I can see the image you uploaded, which contains a series of algebraic expressions that need simplification. I'll solve each expression step by step:

a. 5p+6p3p5p + 6p - 3p

5p+6p3p=(5+63)p=8p5p + 6p - 3p = (5 + 6 - 3)p = 8p

b. 8m3m2m+7m8m - 3m - 2m + 7m

8m3m2m+7m=(832+7)m=10m8m - 3m - 2m + 7m = (8 - 3 - 2 + 7)m = 10m

c. 8x5x+7x8x - 5x + 7x

8x5x+7x=(85+7)x=10x8x - 5x + 7x = (8 - 5 + 7)x = 10x

d. 4xy+6xy3xy2xy4xy + 6xy - 3xy - 2xy

4xy+6xy3xy2xy=(4+632)xy=5xy4xy + 6xy - 3xy - 2xy = (4 + 6 - 3 - 2)xy = 5xy

e. 12y4y+5y12y - 4y + 5y

12y4y+5y=(124+5)y=13y12y - 4y + 5y = (12 - 4 + 5)y = 13y

f. 8k+4k+2k5k8k + 4k + 2k - 5k

8k+4k+2k5k=(8+4+25)k=9k8k + 4k + 2k - 5k = (8 + 4 + 2 - 5)k = 9k

g. 8xy+2xy+5xy8xy + 2xy + 5xy

8xy+2xy+5xy=(8+2+5)xy=15xy8xy + 2xy + 5xy = (8 + 2 + 5)xy = 15xy

h. 9a+2a+3a7a9a + 2a + 3a - 7a

9a+2a+3a7a=(9+2+37)a=7a9a + 2a + 3a - 7a = (9 + 2 + 3 - 7)a = 7a

i. 6m3m+10m6m - 3m + 10m

6m3m+10m=(63+10)m=13m6m - 3m + 10m = (6 - 3 + 10)m = 13m

j. 11p+5p7p11p + 5p - 7p

11p+5p7p=(11+57)p=9p11p + 5p - 7p = (11 + 5 - 7)p = 9p

k. 5a+7a+3a+6a5a + 7a + 3a + 6a

5a+7a+3a+6a=(5+7+3+6)a=21a5a + 7a + 3a + 6a = (5 + 7 + 3 + 6)a = 21a

l. 6ab3abab+2ab6ab - 3ab - ab + 2ab

6ab3abab+2ab=(631+2)ab=4ab6ab - 3ab - ab + 2ab = (6 - 3 - 1 + 2)ab = 4ab

Would you like more details on any of these simplifications, or have further questions? Here are 5 related questions for practice:

  1. Simplify 10x+3x5x10x + 3x - 5x.
  2. What is the result of 7m2m+m6m7m - 2m + m - 6m?
  3. How would you simplify 4p+9p5p4p + 9p - 5p?
  4. Combine like terms for 3ab+6ab2ab3ab + 6ab - 2ab.
  5. Simplify 12a5a+2a6a12a - 5a + 2a - 6a.

Tip: Always group like terms first when simplifying algebraic expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Combining Like Terms

Formulas

Combining like terms by adding or subtracting coefficients of similar terms

Theorems

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Suitable Grade Level

Grades 7-9