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Simplify the following expressions:

a. [tex][tex]$9(x-2)$[/tex][/tex]

b. [tex][tex]$-9(x-2)$[/tex][/tex]

c. [tex][tex]$-(x+2)$[/tex][/tex]

d. [tex][tex]$2(x-7)-(x-9)$[/tex][/tex]

e. [tex][tex]$3y(2x-5)$[/tex][/tex]

f. [tex][tex]$\frac{11}{2}(4a+2b)-(4b-2)$[/tex][/tex]

g. [tex][tex]$-(-3k-9)+5(k-2)$[/tex][/tex]

Sagot :

GinnyAnswer
Laten we elke uitdrukking stap voor stap vereenvoudigen door de haakjes weg te werken:

a. [tex]\( 9(x - 2) \)[/tex]

Stap 1: Distributief toepassen:
[tex]\[ 9(x - 2) = 9x - 18 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ 9x - 18 \][/tex]

b. [tex]\( -9(x - 2) \)[/tex]

Stap 1: Distributief toepassen:
[tex]\[ -9(x - 2) = -9x + 18 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ -9x + 18 \][/tex]

c. [tex]\( -(x + 2) \)[/tex]

Stap 1: Distributief toepassen:
[tex]\[ -(x + 2) = -x - 2 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ -x - 2 \][/tex]

d. [tex]\( 2(x - 7) - (x - 9) \)[/tex]

Stap 1: Distributief toepassen op beide termen:
[tex]\[ 2(x - 7) = 2x - 14 \][/tex]
[tex]\[ -(x - 9) = -x + 9 \][/tex]

Stap 2: Tel de termen bij elkaar op:
[tex]\[ 2x - 14 - x + 9 = x - 5 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ x - 5 \][/tex]

e. [tex]\( 3y(2x - 5) \)[/tex]

Stap 1: Distributief toepassen:
[tex]\[ 3y(2x - 5) = 6xy - 15y \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ 6xy - 15y \][/tex]

f. [tex]\( \frac{11}{2}(4a + 2b) - (4b - 2) \)[/tex]

Stap 1: Distributief toepassen op de breuk en de tweede term:
[tex]\[ \frac{11}{2}(4a + 2b) = \frac{11 \cdot 4a}{2} + \frac{11 \cdot 2b}{2} = 22a + 11b \][/tex]
[tex]\[ -(4b - 2) = -4b + 2 \][/tex]

Stap 2: Tel de termen bij elkaar op:
[tex]\[ 22a + 11b - 4b + 2 = 22a + 7b + 2 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ 22a + 7b + 2 \][/tex]

g. [tex]\( -(-3k - 9) + 5(k - 2) \)[/tex]

Stap 1: Distributief toepassen op beide termen:
[tex]\[ -(-3k - 9) = 3k + 9 \][/tex]
[tex]\[ 5(k - 2) = 5k - 10 \][/tex]

Stap 2: Tel de termen bij elkaar op:
[tex]\[ 3k + 9 + 5k - 10 = 8k - 1 \][/tex]

Dus, de vereenvoudigde vorm is:
[tex]\[ 8k - 1 \][/tex]
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