Find 𝐴 minus 𝐵, given 𝐴 is equal
to five 𝑥 cubed minus three 𝑥 and 𝐵 is equal to negative six 𝑥 squared plus
In order to answer this question,
we need to subtract negative six 𝑥 squared plus three 𝑥 from five 𝑥 cubed minus
three 𝑥. Before we start, it’s important to
remember that we can only collect or group terms with the same exponent or
In this case, the only terms we can
group together are negative three 𝑥 and positive three 𝑥. We also need to remember our rules
when two signs are touching. If we have two positive signs, the
resultant sign is a positive one or an addition sign. When we have a positive and a
negative sign, in either order, our resultant sign is a negative or subtraction
sign. And when we have two negative
signs, the resultant sign is positive or addition.
The only term with 𝑥 cubed in it
is the first one, five 𝑥 cubed. So this too must be in our
answer. We have a negative six 𝑥 squared
term. However, this term is being
subtracted. In other words, we have negative
negative six 𝑥 squared. Two negatives become a
positive. Therefore, this is the same as six
𝑥 squared or positive six 𝑥 squared.
Finally, we need to group the 𝑥
terms, negative three 𝑥 minus positive three 𝑥. This time, our sign will become a
subtraction or negative sign. So we’re left with negative three
𝑥 minus three 𝑥. Negative three minus three is equal
to negative six. Therefore, negative three 𝑥 minus
three 𝑥 equals negative six 𝑥.
This means that if 𝐴 is equal to
five 𝑥 cubed minus three 𝑥 and 𝐵 is equal to negative six 𝑥 squared plus three
𝑥, then 𝐴 minus 𝐵 equals five 𝑥 cubed plus six 𝑥 squared minus six 𝑥.