Solve \left(x^2 3x-1\right) \left(x^2-8x^2\right)

Question

Simplify the expression

- 21 x^{5} + 7 x^{2}

Evaluate

(x^{2} \times 3 x - 1) (x^{2} - 8 x^{2})

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(3 x^{3} - 1) (x^{2} - 8 x^{2})

Subtract the terms

More Steps

Simplify

x^{2} - 8 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 8) x^{2}

Subtract the numbers

- 7 x^{2}

(3 x^{3} - 1) (- 7 x^{2})

Multiply the terms

- 7 x^{2} (3 x^{3} - 1)

Apply the distributive property

- 7 x^{2} \times 3 x^{3} - (- 7 x^{2} \times 1)

Multiply the terms

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Evaluate

- 7 x^{2} \times 3 x^{3}

Multiply the numbers

- 21 x^{2} \times x^{3}

Multiply the terms

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Evaluate

x^{2} \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 3}

Add the numbers

x^{5}

- 21 x^{5}

- 21 x^{5} - (- 7 x^{2} \times 1)

Any expression multiplied by 1 remains the same

- 21 x^{5} - (- 7 x^{2})

Solution

- 21 x^{5} + 7 x^{2}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.693361

Evaluate

(x^{2} \times 3 x - 1) (x^{2} - 8 x^{2})

To find the roots of the expression,set the expression equal to 0

(x^{2} \times 3 x - 1) (x^{2} - 8 x^{2}) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(3 x^{3} - 1) (x^{2} - 8 x^{2}) = 0

Subtract the terms

More Steps

Simplify

x^{2} - 8 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 8) x^{2}

Subtract the numbers

- 7 x^{2}

(3 x^{3} - 1) (- 7 x^{2}) = 0

Multiply the terms

- 7 x^{2} (3 x^{3} - 1) = 0

Change the sign

7 x^{2} (3 x^{3} - 1) = 0

Elimination the left coefficient

x^{2} (3 x^{3} - 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 x^{3} - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 3 x^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{3} - 1 = 0

Move the constant to the right-hand side and change its sign

3 x^{3} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

3 x^{3} = 1

Divide both sides

\frac{3 x ^{3}}{3} = \frac{1}{3}

Divide the numbers

x^{3} = \frac{1}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{3}

Calculate

x = 3 \frac{1}{3}

Simplify the root

More Steps

Evaluate

3 \frac{1}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 3}

Simplify the radical expression

\frac{1}{3 3}

Multiply by the Conjugate

\frac{3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 9}{3}

x = \frac{3 9}{3}

x = 0 x = \frac{3 9}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.693361

Show Solution