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Let’s check out your problem:
Which expression is equivalent to
(
2
g
3
+
4
)
2
(2g^{3}+4)^{2}
(
2
g
3
+
4
)
2
?
\newline
a)
4
9
6
+
16
49^{6}+16
4
9
6
+
16
\newline
b)
4
g
6
+
18
g
3
+
16
4g^{6}+18g^{3}+16
4
g
6
+
18
g
3
+
16
\newline
c)
4
9
6
+
8
49^{6}+8
4
9
6
+
8
\newline
d)
4
g
9
+
16
g
3
+
8
4g^{9}+16g^{3}+8
4
g
9
+
16
g
3
+
8
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Math Problems
Calculus
Find derivatives of using multiple formulae
Full solution
Q.
Which expression is equivalent to
(
2
g
3
+
4
)
2
(2g^{3}+4)^{2}
(
2
g
3
+
4
)
2
?
\newline
a)
4
9
6
+
16
49^{6}+16
4
9
6
+
16
\newline
b)
4
g
6
+
18
g
3
+
16
4g^{6}+18g^{3}+16
4
g
6
+
18
g
3
+
16
\newline
c)
4
9
6
+
8
49^{6}+8
4
9
6
+
8
\newline
d)
4
g
9
+
16
g
3
+
8
4g^{9}+16g^{3}+8
4
g
9
+
16
g
3
+
8
Expand Expression:
Step
1
1
1
: Expand the expression using the formula
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
(a+b)^2 = a^2 + 2ab + b^2
(
a
+
b
)
2
=
a
2
+
2
ab
+
b
2
.
\newline
Calculation: (2g^3 + 4)^2 = (2g^3)^2 + 2\cdot(2g^3)\cdot4 + 4^2\(\newline = 4g^6 + 16g^3 + 16\)
Compare with Options:
Step
2
2
2
: Compare the expanded expression with the given options.
\newline
Calculation:
4
g
6
+
16
g
3
+
16
4g^6 + 16g^3 + 16
4
g
6
+
16
g
3
+
16
matches with one of the options.
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