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Simplify the expression $\left(3x^2-5x+1\right)\left(-8x-5\right)+\left(-4x^2-5x+2\right)\left(6x-5\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$\left(\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}+\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}\right)\left(\sqrt[3]{\left(3x^2-5x+1\right)^{2}}\sqrt[3]{\left(-8x-5\right)^{2}}-\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}+\sqrt[3]{\left(-4x^2-5x+2\right)^{2}}\sqrt[3]{\left(6x-5\right)^{2}}\right)$
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Step-by-step Solution

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  • Simplify
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$

$\left(\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{1}{3}}+\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{1}{3}}\right)\left(\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{2}{3}}-\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{1}{3}}\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{1}{3}}+\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{2}{3}}\right)$

Learn how to solve simplification of algebraic expressions problems step by step online.

$\left(\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{1}{3}}+\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{1}{3}}\right)\left(\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{2}{3}}-\left(\left(3x^2-5x+1\right)\left(-8x-5\right)\right)^{\frac{1}{3}}\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{1}{3}}+\left(\left(-4x^2-5x+2\right)\left(6x-5\right)\right)^{\frac{2}{3}}\right)$

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Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression (3x^2-5x+1)(-8x-5)+(-4x^2-5x+2)(6x-5). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Divide 1 by 3. Divide 1 by 3. Divide 2 by 3.

Final answer to the problem

$\left(\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}+\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}\right)\left(\sqrt[3]{\left(3x^2-5x+1\right)^{2}}\sqrt[3]{\left(-8x-5\right)^{2}}-\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}+\sqrt[3]{\left(-4x^2-5x+2\right)^{2}}\sqrt[3]{\left(6x-5\right)^{2}}\right)$

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Function Plot

Plotting: $\left(\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}+\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}\right)\left(\sqrt[3]{\left(3x^2-5x+1\right)^{2}}\sqrt[3]{\left(-8x-5\right)^{2}}-\sqrt[3]{3x^2-5x+1}\sqrt[3]{-8x-5}\sqrt[3]{-4x^2-5x+2}\sqrt[3]{6x-5}+\sqrt[3]{\left(-4x^2-5x+2\right)^{2}}\sqrt[3]{\left(6x-5\right)^{2}}\right)$

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log◻
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∫◻
|◻|
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: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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