ections: simplify the following expressions by combining like terr corresponding coefficient (note: write subtraction as addition each blank of the “secret code” with the correct letter.
problem\tanswer
$4(x - 5)+3(x + 3)$
$\dfrac{\quad\quad}{d}x + \dfrac{\quad\quad}{g}$
$14x - 3y + 2y - 5x$
$\dfrac{\quad\quad}{m}x + \dfrac{\quad\quad}{u}y$
$2x(4 - 3x)$
$\dfrac{\quad\quad}{b}x^2 + \dfrac{\quad\quad}{q}x$
$6x^2 - 3(x + x^2)$
$\dfrac{\quad\quad}{x}x^2 + \dfrac{\quad\quad}{c}x$
$5x - 6x + 4x - x$
$\dfrac{\quad\quad}{n}x$
$-x(4x + 3y)+x - 4xy$
$\dfrac{\quad\quad}{t}x^2 + \dfrac{\quad\quad}{l}xy + \dfrac{\quad\quad}{y}x$
$7x + 2(5 - x)$
$\dfrac{\quad\quad}{p}x + \dfrac{\quad\quad}{h}$
$3x - 5x(1 + y)$
$\dfrac{\quad\quad}{r}x + \dfrac{\quad\quad}{a}xy$
$7x + 2(3x)-3(x + 2x)-4x$
$\dfrac{\quad\quad}{o}x$
$3x(2 - 3x - 4x^2)$
$\dfrac{\quad\quad}{s}x^3 + \dfrac{\quad\quad}{e}x^2 + \dfrac{\quad\quad}{i}x$

Question

Accepted Answer

### Problem 1: $ 4(x - 5) + 3(x + 3) $
# Explanation:
## Step 1: Distribute the coefficients
$ 4(x - 5) = 4x - 20 $ and $ 3(x + 3) = 3x + 9 $
## Step 2: Combine like terms
$ (4x + 3x) + (-20 + 9) = 7x - 11 $
# Answer:
For $ D $ (coefficient of $ x $): $ 7 $
For $ G $ (constant term): $ -11 $

### Problem 2: $ 14x - 3y + 2y - 5x $
# Explanation:
## Step 1: Combine $ x $-terms
$ 14x - 5x = 9x $
## Step 2: Combine $ y $-terms
$ -3y + 2y = -y $
# Answer:
For $ M $ (coefficient of $ x $): $ 9 $
For $ U $ (coefficient of $ y $): $ -1 $

### Problem 3: $ 2x(4 - 3x) $
# Explanation:
## Step 1: Distribute $ 2x $
$ 2x \cdot 4 - 2x \cdot 3x = 8x - 6x^2 $
## Step 2: Rearrange terms
$ -6x^2 + 8x $
# Answer:
For $ B $ (coefficient of $ x^2 $): $ -6 $
For $ Q $ (coefficient of $ x $): $ 8 $

### Problem 4: $ 6x^2 - 3(x + x^2) $
# Explanation:
## Step 1: Distribute $ -3 $
$ -3(x + x^2) = -3x - 3x^2 $
## Step 2: Combine like terms
$ (6x^2 - 3x^2) + (-3x) = 3x^2 - 3x $
# Answer:
For $ X $ (coefficient of $ x^2 $): $ 3 $
For $ C $ (coefficient of $ x $): $ -3 $

### Problem 5: $ 5x - 6x + 4x - x $
# Explanation:
## Step 1: Combine all $ x $-terms
$ (5 - 6 + 4 - 1)x = 2x $
# Answer:
For $ N $ (coefficient of $ x $): $ 2 $

### Problem 6: $ -x(4x + 3y) + x - 4xy $
# Explanation:
## Step 1: Distribute $ -x $
$ -x \cdot 4x - x \cdot 3y = -4x^2 - 3xy $
## Step 2: Combine like terms
$ -4x^2 + (-3xy - 4xy) + x = -4x^2 - 7xy + x $
# Answer:
For $ T $ (coefficient of $ x^2 $): $ -4 $
For $ L $ (coefficient of $ xy $): $ -7 $
For $ Y $ (coefficient of $ x $): $ 1 $

### Problem 7: $ 7x + 2(5 - x) $
# Explanation:
## Step 1: Distribute $ 2 $
$ 2(5 - x) = 10 - 2x $
## Step 2: Combine like terms
$ (7x - 2x) + 10 = 5x + 10 $
# Answer:
For $ P $ (coefficient of $ x $): $ 5 $
For $ H $ (constant term): $ 10 $

### Problem 8: $ 3x - 5x(1 + y) $
# Explanation:
## Step 1: Distribute $ -5x $
$ -5x(1 + y) = -5x - 5xy $
## Step 2: Combine like terms
$ (3x - 5x) + (-5xy) = -2x - 5xy $
# Answer:
For $ R $ (coefficient of $ x $): $ -2 $
For $ A $ (coefficient of $ xy $): $ -5 $

### Problem 9: $ 7x + 2(3x) - 3(x + 2x) - 4x $
# Explanation:
## Step 1: Simplify each term
$ 2(3x) = 6x $, $ 3(x + 2x) = 3(3x) = 9x $
## Step 2: Combine like terms
$ (7x + 6x - 9x - 4x) = 0x $
# Answer:
For $ O $ (coefficient of $ x $): $ 0 $

### Problem 10: $ 3x(2 - 3x - 4x^2) $
# Explanation:
## Step 1: Distribute $ 3x $
$ 3x \cdot 2 - 3x \cdot 3x - 3x \cdot 4x^2 = 6x - 9x^2 - 12x^3 $
## Step 2: Rearrange terms
$ -12x^3 - 9x^2 + 6x $
# Answer:
For $ S $ (coefficient of $ x^3 $): $ -12 $
For $ E $ (coefficient of $ x^2 $): $ -9 $
For $ I $ (coefficient of $ x $): $ 6 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 4(x - 5) + 3(x + 3) \)

Step 1: Distribute the coefficients

Step 2: Combine like terms

Step 1: Combine \( x \)-terms

Step 2: Combine \( y \)-terms

Step 1: Distribute \( 2x \)

Step 2: Rearrange terms

Answer:

Problem 2: \( 14x - 3y + 2y - 5x \)