simplify each expression.
18. $4x + 5x$
19. $32y - 5y$
20. $4c^2 + 3c + 2c$
21. $5d^2 - 3d^2 + d$
22. $5f^2 + 2f + f^2$
23. $7x + 8x^2 - 3y$
24. $3(p + 9q - 2 + 9) + 14p$
25. $6b + 6b^2 + 4b^3$
26. $2(a^2 + 2b + 2a^2) + b + 2c$

Question

Accepted Answer

# Answer (for each problem):
## 18. $ 9x $
## 19. $ 27y $
## 20. $ 4c^2 + 7c $
## 21. $ 2d^2 + d $
## 22. $ 6f^2 + 2f $ (assuming the middle term is $ 2f $ and the last term is $ +f^2 $, if it's a typo like $ \div $ meant to be $ + $)
## 23. $ 8x^2 + 7x - 3y $
## 24. $ 17p + 27q + 21 $ (simplifying $ 3(p + 9q + 7) + 14p = 3p + 27q + 21 + 14p = 17p + 27q + 21 $)
## 25. $ 4b^3 + 6b^2 + 6b $
## 26. $ 6a^2 + 5b + 2c $ (assuming the original is $ 2(a^2 + 2b + 2a^2) + b + 2c = 2(3a^2 + 2b) + b + 2c = 6a^2 + 4b + b + 2c = 6a^2 + 5b + 2c $, correcting possible typos)

# Explanation (for each step, taking 18 as example, others follow similar combining like terms logic):
## Step 1 (Problem 18): Identify like terms
Like terms are $ 4x $ and $ 5x $ (same variable $ x $, same exponent 1).
## Step 2 (Problem 18): Combine like terms
Add the coefficients: $ 4 + 5 = 9 $, so $ 4x + 5x = 9x $.

(Repeat similar steps for other problems: identify like terms (same variable and exponent), combine their coefficients, handle parentheses by distributing, then combine like terms again.)

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QUESTION IMAGE

Question

Explanation:

Step 1 (Problem 18): Identify like terms

Step 2 (Problem 18): Combine like terms

Answer:

18. \( 9x \)

19. \( 27y \)

20. \( 4c^2 + 7c \)

21. \( 2d^2 + d \)

22. \( 6f^2 + 2f \) (assuming the middle term is \( 2f \) and the last term is \( +f^2 \), if it's a typo like \( \div \) meant to be \( + \))

23. \( 8x^2 + 7x - 3y \)

24. \( 17p + 27q + 21 \) (simplifying \( 3(p + 9q + 7) + 14p = 3p + 27q + 21 + 14p = 17p + 27q + 21 \))

25. \( 4b^3 + 6b^2 + 6b \)

26. \( 6a^2 + 5b + 2c \) (assuming the original is \( 2(a^2 + 2b + 2a^2) + b + 2c = 2(3a^2 + 2b) + b + 2c = 6a^2 + 4b + b + 2c = 6a^2 + 5b + 2c \), correcting possible typos)