Subject: Algebra 1 again

Name: Teresa Who is asking: Student Level: Secondary

Question: I am suppose to subtract the lower polynomial from the one above it.

-3a+11b+2f
-3a-  6b+8f
________________

The answer I came up with is 4b+4f. I would like to know if this answer is correct. If it is wrong would you please explain how to work the problem.

Hi again Teresa,

One way to approach this problem is to write it out explicitly. What I mean is to write "subtract the lower polynomial from the one above it" as

-3a + 11b + 2f - (-3a - 6b + 8f)

Removing the parentheses this expression becomes

-3a + 11b + 2f + 3a + 6b - 8f
= 17b - 6f

If you look at the expression

-3a + 11b + 2f + 3a + 6b - 8f

it is the top equation, minus the bottom expression with all the signs changed. Hence a quicker way to approach this problem is to change the signs of all the terms in the bottom expression and then add. That is subtract

-3a + 11b + 2f
-3a -   6b + 8f
________________

becomes add

-3a + 11b + 2f
+3a +   6b - 8f
________________

 

-3a plus 3a is 0 a's
11b plus 6b is 17b
2f plus -8f is -6f

Hence

-3a + 11b + 2f
-3a -   6b + 8f
________________

is

17b - 6f
Cheers,
Penny
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