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Let’s check out your problem:
Use Pascal's Triangle to complete the expansion of
(
s
+
t
)
3
(s + t)^3
(
s
+
t
)
3
.
\newline
s
3
+
s^3 +
s
3
+
____
s
2
t
+
3
s
t
2
+
t
3
s^2t + 3st^2 + t^3
s
2
t
+
3
s
t
2
+
t
3
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Math Problems
Precalculus
Pascal's triangle and the Binomial Theorem
Full solution
Q.
Use Pascal's Triangle to complete the expansion of
(
s
+
t
)
3
(s + t)^3
(
s
+
t
)
3
.
\newline
s
3
+
s^3 +
s
3
+
____
s
2
t
+
3
s
t
2
+
t
3
s^2t + 3st^2 + t^3
s
2
t
+
3
s
t
2
+
t
3
Pascal's Triangle Coefficients:
Pascal's Triangle for the third row is
1
,
3
,
3
,
1
1, 3, 3, 1
1
,
3
,
3
,
1
. These numbers are the coefficients for the expansion.
Second Term Coefficient:
The second term in the expansion will have the coefficient
3
3
3
from Pascal's Triangle, so it's
3
s
2
t
3s^2t
3
s
2
t
.
Full Expansion:
Now, write down the full expansion using the coefficients:
s
3
+
3
s
2
t
+
3
s
t
2
+
t
3
s^3 + 3s^2t + 3st^2 + t^3
s
3
+
3
s
2
t
+
3
s
t
2
+
t
3
.
More problems from Pascal's triangle and the Binomial Theorem
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Find the degree of this polynomial.
\newline
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\newline
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\newline
(
9
a
+
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−
(
2
a
+
4
)
(9a + 5) - (2a + 4)
(
9
a
+
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)
−
(
2
a
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)
\newline
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Find the product. Simplify your answer.
\newline
−
3
v
2
(
v
2
−
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)
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−
3
v
2
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v
2
−
9
)
\newline
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Find the product. Simplify your answer.
\newline
(
v
−
3
)
(
4
v
+
1
)
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(
v
−
3
)
(
4
v
+
1
)
\newline
______
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Question
Find the square. Simplify your answer.
\newline
(
3
y
+
2
)
2
(3y + 2)^2
(
3
y
+
2
)
2
\newline
______
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Posted 5 months ago
Question
Divide. If there is a remainder, include it as a simplified fraction.
\newline
(
24
t
2
+
36
t
)
÷
6
t
(24t^2 + 36t) \div 6t
(
24
t
2
+
36
t
)
÷
6
t
\newline
______
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Posted 5 months ago
Question
Is the function
q
(
x
)
=
x
6
−
9
q(x) = x^6 - 9
q
(
x
)
=
x
6
−
9
even, odd, or neither?
\newline
Choices:
\newline
[[even][odd][neither]]
\text{[[even][odd][neither]]}
[[even][odd][neither]]
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Posted 9 months ago
Question
Find the product. Simplify your answer.
\newline
−
3
q
2
(
−
3
q
2
+
q
)
-3q^2(-3q^2 + q)
−
3
q
2
(
−
3
q
2
+
q
)
\newline
______
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Posted 9 months ago
Question
Find the product. Simplify your answer.
\newline
(
r
+
3
)
(
4
r
+
2
)
(r + 3)(4r + 2)
(
r
+
3
)
(
4
r
+
2
)
\newline
______
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Posted 9 months ago
Question
Find the roots of the factored polynomial.
\newline
(
x
+
7
)
(
x
+
4
)
(x + 7)(x + 4)
(
x
+
7
)
(
x
+
4
)
\newline
Write your answer as a list of values separated by commas.
\newline
x
=
x =
x
=
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Posted 9 months ago
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