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)

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)

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)

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)

• Question 2
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Simplify

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

• Question 3
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Simplify

½(10a - 2) - (2a - 5)

• Question 4
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Simplify

2(15a - 15) + ½(10a + 12)

• Question 5
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Simplify

2(3a + 12) - ½(12a - 12)

• Question 6
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Simplify

¼(40a + 8) - 2(5a - 1)

• Question 7
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Simplify

¾(4a + 8) - 2(-5a + 1)

• Question 8
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Simplify

½(3a + 2) - ½(6 + a)

• Question 9
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Simplify

½(3a + 1) - ½(3 - a)

• Question 10
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Simplify

¾(3a + 1) + ¼(9 - a)