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Example 1
3(x + 2) + 5(x + 4)
= 3(x) + 3(+2) + 5(x) + 5(+4)
= 3x + 6 + 5x + 20
= 3x + 5x + 6 + 20
= 8x + 26
One way in which students understand more clearly
is to write in more positive signs
So we could get
3(x + 2) + 5(x + 4)
= +3(+x + 2) + 5(+x + 4)
= +3(+x) + 3(+2) + 5(+x) + 5(+4)
= +3x + 6 + 5x + 20
= +3x + 5x + 6 + 20
= +8x + 26
= 8x + 26
Example 2
3(x + 2) - 5(x + 4)
= 3(x) + 3(+2) - 5(x) - 5(+4)
= 3x + 6 - 5x - 20
= 3x - 5x + 6 - 20
= - 2x - 14
Example 3
3(x - 2) - 5(x + 4)
= 3(x) + 3(-2) - 5(x) - 5(+4)
= 3x - 6 - 5x - 20
= 3x - 5x - 6 - 20
= - 2x - 26
Example 4
3(x - 2) - 5(x - 4)
= 3(x) + 3(-2) - 5(x) - 5(-4)
= 3x - 6 - 5x + 20
= 3x - 5x - 6 + 20
= - 2x + 14
Example 5
- 3(x - 2) - 5(x - 4)
= - 3(x) - 3(-2) - 5(x) - 5(-4)
= - 3x + 6 - 5x + 20
= - 3x - 5x + 6 + 20
= - 8x + 26
Example 6
- 3(x - 2) - 5(-x - 4)
= - 3(x) - 3(-2) - 5(-x) - 5(-4)
= - 3x + 6 + 5x + 20
= - 3x + 5x + 6 + 20
= 2x + 26
Example 7
- 3(-x - 2) - 5(-x - 4)
= - 3(-x) - 3(-2) - 5(-x) - 5(-4)
= 3x + 6 + 5x + 20
= 3x + 5x + 6 + 20
= 8x + 26
Notice that this result
for the example
where all of the initial signs are negative
IS EXACTLY THE SAME RESULT
as when all of the initial signs are positive
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