$f\left(x\right)=\left(4x^2+4x+5\right)^3$

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Final answer to the problem

$f\left(x\right)=64x^{6}+192x^{5}+432x^{4}+544x^{3}+540x^2+125+300x$
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Apply the formula: $\left(a+b+c\right)^3$$=a^3+3a^2b+3a^2c+b^3+3ab^2+3b^2c+c^3+3ac^2+3bc^2+6abc$, where $a=4x^2$, $b=4x$ and $c=5$

$f\left(x\right)=\left(4x^2\right)^3+12\left(4x^2\right)^2x+15\left(4x^2\right)^2+\left(4x\right)^3+12x^2\left(4x\right)^2+15\left(4x\right)^2+125+300x^2+300x+480x^2x$

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$f\left(x\right)=\left(4x^2\right)^3+12\left(4x^2\right)^2x+15\left(4x^2\right)^2+\left(4x\right)^3+12x^2\left(4x\right)^2+15\left(4x\right)^2+125+300x^2+300x+480x^2x$

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Learn how to solve problems step by step online. f(x)=(4x^2+4x+5)^3. Apply the formula: \left(a+b+c\right)^3=a^3+3a^2b+3a^2c+b^3+3ab^2+3b^2c+c^3+3ac^2+3bc^2+6abc, where a=4x^2, b=4x and c=5. Apply the formula: x\cdot x^n=x^{\left(n+1\right)}, where x^nx=480x^2x, x^n=x^2 and n=2. Apply the formula: \left(ab\right)^n=a^nb^n, where a=4, b=x and n=2. Apply the formula: \left(ab\right)^n=a^nb^n.

Final answer to the problem

$f\left(x\right)=64x^{6}+192x^{5}+432x^{4}+544x^{3}+540x^2+125+300x$

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Function Plot

Plotting: $f\left(x\right)-\left(4x^2+4x+5\right)^3$

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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