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Find the discriminant of the equation $a\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)^2$

Step-by-step Solution

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Final answer to the problem

$a\left(b^{2}s^{6}x^{2}+4bs^3xy-21y^{2}-16x^{2}-40xy\right)^2$
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Step-by-step Solution

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Expand the expression $\left(bs^3x+2y\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$

$a\left(b^{2}s^{6}x^{2}+4bs^3xy+4y^{2}-\left(4x+5y\right)^2\right)^2$

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$a\left(b^{2}s^{6}x^{2}+4bs^3xy+4y^{2}-\left(4x+5y\right)^2\right)^2$

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Learn how to solve discriminant of quadratic equation problems step by step online. Find the discriminant of the equation a((bs^3x+2y)^2-(4x+5y)^2)^2. Expand the expression \left(bs^3x+2y\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Expand the expression \left(4x+5y\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term -1 by each term of the polynomial \left(16x^{2}+40xy+25y^{2}\right). Combining like terms 4y^{2} and -25y^{2}.

Final answer to the problem

$a\left(b^{2}s^{6}x^{2}+4bs^3xy-21y^{2}-16x^{2}-40xy\right)^2$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind a((bs^3+2y)^2+-1(4x+5y)^2)^2 using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even points

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Plotting: $a\left(b^{2}s^{6}x^{2}+4bs^3xy-21y^{2}-16x^{2}-40xy\right)^2$

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0
a
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g
m
n
u
v
w
x
y
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.
(◻)
+
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×
◻/◻
/
÷
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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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.

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