Find the discriminant of the equation $\left(x^2-a^2\right)^2\left(x^3+a^3\right)^3\left(x^2+ax+a^2\right)^2$

Step-by-step Solution

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Final answer to the problem

$\left(x^{4}-2x^2a^2+a^{4}\right)\left(x^3+a^3\right)^3\left(x^2+ax+a^2\right)^2$
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Step-by-step Solution

How should I solve this problem?

  • Find the discriminant
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
  • Load more...
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1

Expand $\left(x^2-a^2\right)^2$

$\left(x^{4}-2x^2a^2+a^{4}\right)\left(x^3+a^3\right)^3\left(x^2+ax+a^2\right)^2$

Final answer to the problem

$\left(x^{4}-2x^2a^2+a^{4}\right)\left(x^3+a^3\right)^3\left(x^2+ax+a^2\right)^2$

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Function Plot

Plotting: $\left(x^{4}-2x^2a^2+a^{4}\right)\left(x^3+a^3\right)^3\left(x^2+ax+a^2\right)^2$

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1
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4
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

How to improve your answer:

Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.

Used Formulas

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