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Simplify the expression $f\left(x\right)=\left(4x^3+2x^2-x-3\right)^2$

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Solution

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Final answer to the problem

$f\left(x\right)=16x^{6}-4x^{4}-11x^2+6x+9+16x^{5}-28x^{3}$
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Step-by-step Solution

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  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
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  • Factor by completing the square
  • Find the roots
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Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

Learn how to solve special products problems step by step online.

$f\left(x\right)=\left(4x^3\right)^2+\left(2x^2\right)^2+\left(-x-3\right)^2+16x^3x^2+8x^3\left(-x-3\right)+4x^2\left(-x-3\right)$

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Unlock the first 3 steps of this solution

Learn how to solve special products problems step by step online. Simplify the expression f(x)=(4x^3+2x^2-x+-3)^2. Expand the trinomial using the formula \left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. When multiplying exponents with same base we can add the exponents. The power of a product is equal to the product of it's factors raised to the same power. Multiply the single term 8x^3 by each term of the polynomial \left(-x-3\right).

Final answer to the problem

$f\left(x\right)=16x^{6}-4x^{4}-11x^2+6x+9+16x^{5}-28x^{3}$

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Function Plot

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

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x
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.
(◻)
+
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×
◻/◻
/
÷
◻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

How to improve your answer:

Similar Problems Solved

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$\left(2a^6-6a^3\right)^2$

Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

Used Formulas

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