how do you expand and simplify 2(a+5)+3(4-a)  

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll use the property of multiplication of being distributive over addition, such as:

2(a+5) = 2*a + 2*5

2(a+5) = 2a + 10 (1)

3(4-a) = 3*4 + 3*(-a)

3(4-a) = 12 - 3a (2)

Now, we'll add  (1) + (2):

2a + 10 + 12 - 3a

We'll combine the terms that contain a and the numbers alone:

(2a - 3a) + (10 + 12) = -a + 22

The result of the given expression is: 2(a+5) + 3(4-a) = 22 - a.

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

 2 ( a + 5 ) + 3 ( 4 - a )

Distribute the 2 and the 3 First

By distributing, you should get

2a + 10 + 12 - 3a now combine the like terms ( 2a with -3a and 10 with 12 )

By combining, the like terms, you should get

22 - a which is your answer

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

2(a+5)+3(4-a)

use the distributive property on the 2 and distribute it to the numbers in the first parenthesis:

2a + 10 + 3(4-a)

do the same thing for the 3

2a + 10 + 12 - 3a

now combine the like terms

10 + 12 + 2a - 3a

add them up

22 - a

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

2(a+5)+3(4-a) 

We can use the distributive property twice to get the answer. 

 ( 2a + 10 )  +  ( 12 - 3a )

Now combine like terms

22 - a

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