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
