Binomials (Adding and Subtracting) (3)
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  • Introduction
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A binomial expression is one that has two terms, such as 3a - 1

When we add and subtract binomials, we combine the letter terms and the numbers separately.

If there is a number outside a bracket, it multiplies everything inside that bracket.

Be careful with - signs and try to put the letter term first

(i.e. 3a -1 rather than -1 + 3a).

 

Example 1

Simplify

4(3a - 1) - (2a + 7)

 

Answer

4(3a - 1) - 1(2a + 7)

= 12a - 4 - 2a - 7

= 12a - 2a - 4 - 7

= 10a - 11

 

Example 2

Simplify

5(3a - 1) - 3(2a - 7)

 

Answer

5(3a - 1) - 3(2a - 7)

= 15a - 5 - 6a + 21

= 15a - 6a - 5 + 21

= 9a + 16

 

Example 3

Simplify

½(4a + 12) - 3(2 - 7a)

 

Answer

½(4a + 12) - 3(2 - 7a)

= 2a + 6 - 6 + 21a

= 2a + 21a + 6 - 6

= 23a

  • Question 1
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Simplify

 

3(4a - 12) + (2a + 5)

 

(Write your answer without spaces)

  • Question 2
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Simplify

 

(13a - 12) - 2(2a + 15)

 

(Write your answer without spaces)

  • Question 3
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Simplify

 

½(10a - 2) - (2a - 5)

 

(Write your answer without spaces)

  • Question 4
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Simplify

 

2(15a - 15) + ½(10a + 12)

 

(Write your answer without spaces)

  • Question 5
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Simplify

 

2(3a + 12) - ½(12a - 12)

 

(Write your answer without spaces)

  • Question 6
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Simplify

 

¼(40a + 8) - 2(5a - 1)

 

(Write your answer without spaces)

  • Question 7
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Simplify

 

¾(4a + 8) - 2(-5a + 1)

 

(Write your answer without spaces)

  • Question 8
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Simplify

 

½(3a + 2) - ½(6 + a)

 

(Write your answer without spaces)

  • Question 9
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Simplify

 

½(3a + 1) - ½(3 - a)

 

(Write your answer without spaces)

  • Question 10
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Simplify

 

¾(3a + 1) + ¼(9 - a)

 

(Write your answer without spaces)

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