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Simplify the expression $\frac{y^4-256}{y+4}$

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Solution

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Final answer to the problem

$\left(y^{2}+16\right)\left(y-4\right)$
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Step-by-step Solution

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Simplify $\sqrt{y^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{2}$

$\frac{\left(y^{2}+\sqrt{256}\right)\left(\sqrt{y^4}-\sqrt{256}\right)}{y+4}$

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$\frac{\left(y^{2}+\sqrt{256}\right)\left(\sqrt{y^4}-\sqrt{256}\right)}{y+4}$

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Learn how to solve implicit differentiation problems step by step online. Simplify the expression (y^4-256)/(y+4). Simplify \sqrt{y^4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{2}. Calculate the power \sqrt{256}. Simplify \sqrt{y^4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{2}. Calculate the power \sqrt{256}.

Final answer to the problem

$\left(y^{2}+16\right)\left(y-4\right)$

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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

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (y^4-256)/(y+4) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Plotting: $\left(y^{2}+16\right)\left(y-4\right)$

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

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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