Solve x^2 (x 8)-x(x 8)-6(x 8)

Question

Simplify the expression

8 x^{3} - 8 x^{2} - 48 x

Evaluate

x^{2} (x \times 8) - x (x \times 8) - 6 (x \times 8)

Remove the parentheses

x^{2} \times x \times 8 - x \times x \times 8 - 6 x \times 8

Multiply

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Multiply the terms

x^{2} \times x \times 8

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 8

Add the numbers

x^{3} \times 8

Use the commutative property to reorder the terms

8 x^{3}

8 x^{3} - x \times x \times 8 - 6 x \times 8

Multiply

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Multiply the terms

- x \times x \times 8

Multiply the terms

- x^{2} \times 8

Use the commutative property to reorder the terms

- 8 x^{2}

8 x^{3} - 8 x^{2} - 6 x \times 8

Solution

8 x^{3} - 8 x^{2} - 48 x

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Factor the expression

8 x (x - 3) (x + 2)

Evaluate

x^{2} (x \times 8) - x (x \times 8) - 6 (x \times 8)

Remove the parentheses

x^{2} \times x \times 8 - x \times x \times 8 - 6 x \times 8

Use the commutative property to reorder the terms

x^{2} \times 8 x - x \times x \times 8 - 6 x \times 8

Multiply the terms

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Evaluate

x^{2} \times 8 x

Use the commutative property to reorder the terms

8 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

8 x^{3}

8 x^{3} - x \times x \times 8 - 6 x \times 8

Use the commutative property to reorder the terms

8 x^{3} - x \times 8 x - 6 x \times 8

Multiply the terms

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Evaluate

x \times 8 x

Use the commutative property to reorder the terms

8 x \times x

Multiply the terms

8 x^{2}

8 x^{3} - 8 x^{2} - 6 x \times 8

Use the commutative property to reorder the terms

8 x^{3} - 8 x^{2} - 6 \times 8 x

Multiply the numbers

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Evaluate

6 \times 8

Multiply the numbers

48

Evaluate

48 x

8 x^{3} - 8 x^{2} - 48 x

Rewrite the expression

8 x \times x^{2} - 8 x \times x - 8 x \times 6

Factor out 8 x from the expression

8 x (x^{2} - x - 6)

Solution

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Evaluate

x^{2} - x - 6

Rewrite the expression

x^{2} + (2 - 3) x - 6

Calculate

x^{2} + 2 x - 3 x - 6

Rewrite the expression

x \times x + x \times 2 - 3 x - 3 \times 2

Factor out x from the expression

x (x + 2) - 3 x - 3 \times 2

Factor out - 3 from the expression

x (x + 2) - 3 (x + 2)

Factor out x + 2 from the expression

(x - 3) (x + 2)

8 x (x - 3) (x + 2)

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Find the roots

x_{1} = - 2, x_{2} = 0, x_{3} = 3

Evaluate

x^{2} (x \times 8) - x (x \times 8) - 6 (x \times 8)

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

x^{2} (x \times 8) - x (x \times 8) - 6 (x \times 8) = 0

Use the commutative property to reorder the terms

x^{2} \times 8 x - x (x \times 8) - 6 (x \times 8) = 0

Use the commutative property to reorder the terms

x^{2} \times 8 x - x \times 8 x - 6 (x \times 8) = 0

Use the commutative property to reorder the terms

x^{2} \times 8 x - x \times 8 x - 6 \times 8 x = 0

Multiply the terms

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Evaluate

x^{2} \times 8 x

Use the commutative property to reorder the terms

8 x^{2} \times x

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

8 x^{3}

8 x^{3} - x \times 8 x - 6 \times 8 x = 0

Multiply the terms

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Evaluate

x \times 8 x

Use the commutative property to reorder the terms

8 x \times x

Multiply the terms

8 x^{2}

8 x^{3} - 8 x^{2} - 6 \times 8 x = 0

Multiply the numbers

8 x^{3} - 8 x^{2} - 48 x = 0

Factor the expression

8 x (x - 3) (x + 2) = 0

Divide both sides

x (x - 3) (x + 2) = 0

Separate the equation into 3 possible cases

x = 0 x - 3 = 0 x + 2 = 0

Solve the equation

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Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3 x + 2 = 0

Solve the equation

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Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = 0 x = 3 x = - 2

Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 3

Show Solution