Question

name glenda li
date sep 25
level 1: distribute once only
distributive property
directions: circle the color of the simplified algebraic expression for each problem.
1 5(3x - 5) 25 - 15x blue 15x - 25 white 15x + 25 black -15x - 25 orange
2 -2(8 - 7x) 16 - 14x red -16 - 14x yellow -14x + 16 pink 14x - 16 green
3 16(2 - x) -16x + 32 purple 32x - 16 black 16x - 32 green -16x - 32 blue
4 -(5x + 9) -5x + 9 maroon -5x - 9 orange 9 + 5x aqua 5x + 9 yellow
5 -4(10x - 3) 40x + 7 yellow -40x + 7 red -40x + 12 pink 40x - 12 green
6 -2(x + 7) -2x - 14 blue -2x + 5 purple 2x - 14 red -2x + 14 orange
7 -(6x - 1) 6x + 1 aqua -1 - 6x white 6x - 1 brown -6x + 1 red
8 -3(2x + 9) 6x - 27 gray -6x + 27 dark pink 27 + 6x yellow -6x - 27 dark green
9 10(5 - 9x) -50 + 90x light blue 50 + 90x aqua -90x + 50 black 90x - 50 teal
10 2(3x + 4) 6x + 6 maroon 6x + 8 light blue 5x + 6 purple 6x + 4 yellow
11 -5(12 - 5x) 60 - 25x aqua 25x - 60 yellow -60 - 25x white -25x + 60 dark red
12 -8(2x + 4) -16x - 32 light purple 16x + 32 maroon -32 + 16x gray 32 - 16x brown
13 5(12x - 3) 60 - 15x pink 60x - 3 light purple 60x - 15 light green 15 - 60x blue
14 -7(9 - x) 63 - 7x color 7x - 63 dark orange -63 - x brown 7x + 6 white
15 3(8x - 5) 24x - 15 dark yellow 15 - 24x red 15 + 24x dark pink 24x - 15 light
16 2(x - 7) 2x - 7 red 2x + 14 green 2 - 14x light purple 2x - 14 maroon

Explanation:

Step1: Apply distributive property

The distributive property is \(a(b + c)=ab+ac\) or \(a(b - c)=ab - ac\).

1. For \(5(3x - 5)\), we have \(5\times3x-5\times5 = 15x-25\) (WHITE).
2. For \(-2(8 - 7x)\), we get \(-2\times8-(-2)\times7x=-16 + 14x=14x - 16\) (GREEN).
3. For \(16(2 - x)\), it is \(16\times2-16\times x = 32-16x=-16x + 32\) (PURPLE).
4. For \(-(5x + 9)\), we have \(-1\times5x-1\times9=-5x - 9\) (ORANGE).
5. For \(-4(10x - 3)\), we get \(-4\times10x-(-4)\times3=-40x + 12\) (PINK).
6. For \(-2(x + 7)\), it is \(-2\times x-2\times7=-2x - 14\) (BLUE).
7. For \(-(6x - 1)\), we have \(-1\times6x-(-1)\times1=-6x + 1\) (RED).
8. For \(-3(2x + 9)\), we get \(-3\times2x-3\times9=-6x - 27\) (DARK GREEN).
9. For \(10(5 - 9x)\), it is \(10\times5-10\times9x = 50-90x=-90x + 50\) (BLACK).
10. For \(2(3x + 4)\), we have \(2\times3x+2\times4 = 6x+8\) (LIGHT BLUE).
11. For \(-5(12 - 5x)\), we get \(-5\times12-(-5)\times5x=-60 + 25x=25x - 60\) (YELLOW).
12. For \(-8(2x + 4)\), it is \(-8\times2x-8\times4=-16x - 32\) (LIGHT PURPLE).
13. For \(5(12x - 3)\), we have \(5\times12x-5\times3 = 60x-15\) (LIGHT GREEN).
14. For \(-7(9 - x)\), we get \(-7\times9-(-7)\times x=-63 + 7x=7x - 63\) (DARK ORANGE).
15. For \(3(8x - 5)\), it is \(3\times8x-3\times5 = 24x-15\) (DARK YELLOW).
16. For \(2(x - 7)\), we have \(2\times x-2\times7=2x - 14\) (RED).

Answer:

1. WHITE
2. GREEN
3. PURPLE
4. ORANGE
5. PINK
6. BLUE
7. RED
8. DARK GREEN
9. BLACK
10. LIGHT BLUE
11. YELLOW
12. LIGHT PURPLE
13. LIGHT GREEN
14. DARK ORANGE
15. DARK YELLOW
16. RED