Question

name
combining like terms
directions: simplify the expressions. circle the color of your answer choice and color
the areas with the corresponding problem numbers on the coloring sheet.
1 $3x + 10 - 8 + 2x$
13x - 6
green
5x + 2
brown
5x - 2
pink
2x + 5
white
2 $x + 4 - x$
2x + 4
purple
4x
maroon
x + 4
brown
4
yellow
3 $5x + x + 2$
6x + 2
black
5x + 2
dark red
5x + 3
blue
7x
yellow
4 $9 - 9x + 1$
-9x + 10
orange
x + 1
pink
1
light blue
9x - 10
turquoise
5 $x + 3 + x + 3$
6x
light green
6x²
purple
2x + 6
red - orange
x + 6
black
6 $15 - 10 + x$
5x
gray
x + 5
brown
5 - x
silver
x - 5
dark blue
7 $1 + 2x + 3x - 8$
5x - 7
white
5x + 7
turquoise
5x + 9
blue
5x - 9
green
8 $16x - 5x + 2 - 11x$
22x + 2
orange
2x
pink
2
green
x + 2
light pink
9 $x - x - x - x$
-4x
yellow
4x
gold
x - 3
light blue
-2x
purple
10 $1 - 3 - x - 9$
11 - x
light green
x - 11
dark blue
-x - 13
black
-x - 11
gray
11 $x + y + x + y$
xyxy
dark red
2x + 2y
white
x²y²
silver
x + y
orange
12 $-y + 1 + x$
-x + y + 1
light pink
x - y + 1
blue
-xy
green
1x - y
gold
13 $7 - 13x + y - 7 + 13x - y$
x + y
light blue
0
dark red
-26x + y
yellow
1
brown
14 $x² + 2x + 3x + 9$
6x² + 9
green
6x + 9
dark blue
x² + 5x + 9
dark green
5x + 9
turquoise
15 $x² - 4x + 4x - 16$
x² - 16
light brown
x² - 8x - 16
white
x² + 8x - 16
light green
x² + 16
gold
16 $9x² + x - 3x + 1$
9x² + 2x + 1
silver
9x² - 4x + 1
light pink
9x² + 4x + 1
purple
9x² - 2x + 1
yellow
17 $3x² - x + 5 - 7x² + 2x + 1$
10x² + x + 6
purple
4x² - 3x + 6
turquoise
-4x² + x + 6
black
-4x² - x + 6
dark red
18 $xy + yx$
x²y²
dark blue
2x + 2y
purple
2xy
dark brown
2x²y²
green
19 $7y² + 5x² + 5y²$
17x²y²
yellow
5x² + 12y²
red - orange
10x² + 7y²
green
12x² + 5y²
light blue
20 $3xy + 5xy - 2x + y$
8xy - 2x + y
red
10xy + y
dark red
3xy + 3x + y
orange
7xy
black

Answer:

Let's solve each problem one by one by combining like terms:

Problem 1: \( 3x + 10 - 8 + 2x \)

Step 1: Combine like terms for \( x \)

\( 3x + 2x = 5x \)

Step 2: Combine constant terms

\( 10 - 8 = 2 \)

Step 3: Combine results

\( 5x + 2 \) (BROWN)

Problem 2: \( x + 4 - x \)

Step 1: Combine like terms for \( x \)

\( x - x = 0 \)

Step 2: Combine with constant term

\( 0 + 4 = 4 \) (YELLOW)

Problem 3: \( 5x + x + 2 \)

Step 1: Combine like terms for \( x \)

\( 5x + x = 6x \)

Step 2: Combine with constant term

\( 6x + 2 \) (BLACK)

Problem 4: \( 9 - 9x + 1 \)

Step 1: Combine constant terms

\( 9 + 1 = 10 \)

Step 2: Combine with \( x \) term

\( -9x + 10 \) (ORANGE)

Problem 5: \( x + 3 + x + 3 \)

Step 1: Combine like terms for \( x \)

\( x + x = 2x \)

Step 2: Combine constant terms

\( 3 + 3 = 6 \)

Step 3: Combine results

\( 2x + 6 \) (RED - ORANGE)

Problem 6: \( 15 - 10 + x \)

Step 1: Combine constant terms

\( 15 - 10 = 5 \)

Step 2: Combine with \( x \) term

\( x + 5 \) (BROWN) Wait, no: \( 15 - 10 = 5 \), so \( 5 + x = x + 5 \)? Wait, the options have \( 5x \) (GRAY) or \( x + 5 \) (BROWN). Wait, \( 15 - 10 = 5 \), so \( 5 + x = x + 5 \), which is \( x + 5 \) (BROWN). Wait, but let's check again: \( 15 - 10 = 5 \), so \( 5 + x = x + 5 \), which is option BROWN (\( x + 5 \)).

Problem 7: \( 1 + 2x + 3x - 8 \)

Step 1: Combine like terms for \( x \)

\( 2x + 3x = 5x \)

Step 2: Combine constant terms

\( 1 - 8 = -7 \)

Step 3: Combine results

\( 5x - 7 \) (WHITE)

Problem 8: \( 16x - 5x + 2 - 11x \)

Step 1: Combine like terms for \( x \)

\( 16x - 5x - 11x = 0 \)

Step 2: Combine with constant term

\( 0 + 2 = 2 \) (GREEN)

Problem 9: \( x - x - x - x \)

Step 1: Combine like terms for \( x \)

\( x - x - x - x = -2x \) (PURPLE)

Problem 10: \( 1 - 3 - x - 9 \)

Step 1: Combine constant terms

\( 1 - 3 - 9 = -11 \)

Step 2: Combine with \( x \) term

\( -x - 11 \) (GRAY)

Problem 11: \( x + y + x + y \)

Step 1: Combine like terms for \( x \)

\( x + x = 2x \)

Step 2: Combine like terms for \( y \)

\( y + y = 2y \)

Step 3: Combine results

\( 2x + 2y \) (WHITE)

Problem 12: \( -y + 1 + x \)

Step 1: Rearrange terms

\( x - y + 1 \) (GOLD)

Problem 13: \( 7 - 13x + y - 7 + 13x - y \)

Step 1: Combine like terms for \( x \)

\( -13x + 13x = 0 \)

Step 2: Combine like terms for \( y \)

\( y - y = 0 \)

Step 3: Combine constant terms

\( 7 - 7 = 0 \)

Step 4: Combine results

\( 0 \) (DARK RED)

Problem 14: \( x^2 + 2x + 3x + 9 \)

Step 1: Combine like terms for \( x \)

\( 2x + 3x = 5x \)

Step 2: Combine with \( x^2 \) and constant term

\( x^2 + 5x + 9 \) (DARK GREEN)

Problem 15: \( x^2 - 4x + 4x - 16 \)

Step 1: Combine like terms for \( x \)

\( -4x + 4x = 0 \)

Step 2: Combine with \( x^2 \) and constant term

\( x^2 - 16 \) (LIGHT BROWN)

Problem 16: \( 9x^2 + x - 3x + 1 \)

Step 1: Combine like terms for \( x \)

\( x - 3x = -2x \)

Step 2: Combine with \( x^2 \) and constant term

\( 9x^2 - 2x + 1 \) (YELLOW)

Problem 17: \( 3x^2 - x + 5 - 7x^2 + 2x + 1 \)

Step 1: Combine like terms for \( x^2 \)

\( 3x^2 - 7x^2 = -4x^2 \)

Step 2: Combine like terms for \( x \)

\( -x + 2x = x \)

Step 3: Combine constant terms

\( 5 + 1 = 6 \)

Step 4: Combine results

\( -4x^2 + x + 6 \) (BLACK)

Problem 18: \( xy + yx \)

Step 1: Combine like terms (since \( xy = yx \))

\( xy + yx = 2xy \) (DARK BROWN)

Problem 19: \( 7y^2 + 5x^2 + 5y^2 \)

Step 1: Combine like terms for \( y^2 \)

\( 7y^2 + 5y^2 = 12y^2 \)

Step 2: Combine with \( x^2 \) term

\( 5x^2 + 12y^2 \) (RED - ORANGE)

Problem 20: \( 3xy + 5xy - 2x + y \)

Step 1: Combine like terms for \( xy \)

\( 3xy + 5xy = 8xy \)

Step 2: Combine with \( x \) and \( y \) terms

\( 8xy - 2x + y \) (RED)

These are the solutions for each problem by combining like terms.