Makakuha ng eksaktong mga sagot sa iyong mga tanong sa IDNStudy.com. Sumali sa aming platform ng tanong at sagot upang makatanggap ng mabilis at eksaktong tugon mula sa mga propesyonal sa iba't ibang larangan.
Answer:
to do...
Look at each possible power of
x
in descending order and add up the different ways of getting it.
So in our example:
Given:
(
x
+
1
)
(
x
2
+
x
+
1
)
we can tell that the highest possible power of
x
in the product is
3
, so work down from there:
x
3
: This can only result from multiplying the
x
in the binomial by the
x
2
in the trinomial, so the coefficient is:
1
⋅
1
=
1
So we can start to write:
(
x
+
1
)
(
x
2
+
x
+
1
)
=
x
3
...
x
2
: This can result from
x
⋅
x
or
1
⋅
x
2
, so the coefficient is:
1
⋅
1
+
1
⋅
1
=
2
So we can add
+
2
x
2
to the result:
(
x
+
1
)
(
x
2
+
x
+
1
)
=
x
3
+
2
x
2
...
x
1
:
This can result from
x
⋅
1
or
1
⋅
x
, so the coefficient is:
1
⋅
1
+
1
⋅
1
=
2
So we can add
+
2
x
to the result:
(
x
+
1
)
(
x
2
+
x
+
1
)
=
x
3
+
2
x
2
+
2
x
...
x
0
:
The constant term can only result from multiplying the constant term of the binomial by that of the trinomial, so:
1
⋅
1
=
1
So our final result is:
(
x
+
1
)
(
x
2
+
x
+
1
)
=
x
3
+
2
x
2
+
2
x
+
1
In practice (and with practice) the result line is all you need write: Adding up the coefficients can be done in your head