Solve 3x^312x -36

Question

Simplify the expression

36 x^{4} - 36

Evaluate

3 x^{3} \times 12 x - 36

Solution

More Steps

Evaluate

3 x^{3} \times 12 x

Multiply the terms

36 x^{3} \times x

Multiply the terms with the same base by adding their exponents

36 x^{3 + 1}

Add the numbers

36 x^{4}

36 x^{4} - 36

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Factor the expression

36 (x - 1) (x + 1) (x^{2} + 1)

Evaluate

3 x^{3} \times 12 x - 36

Evaluate

More Steps

Evaluate

3 x^{3} \times 12 x

Multiply the terms

36 x^{3} \times x

Multiply the terms with the same base by adding their exponents

36 x^{3 + 1}

Add the numbers

36 x^{4}

36 x^{4} - 36

Factor out 36 from the expression

36 (x^{4} - 1)

Factor the expression

More Steps

Evaluate

x^{4} - 1

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x^{2} - 1) (x^{2} + 1)

36 (x^{2} - 1) (x^{2} + 1)

Solution

More Steps

Evaluate

x^{2} - 1

Rewrite the expression in exponential form

x^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x - 1) (x + 1)

36 (x - 1) (x + 1) (x^{2} + 1)

Show Solution

Find the roots

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

Evaluate

3 x^{3} \times 12 x - 36

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

3 x^{3} \times 12 x - 36 = 0

Multiply

More Steps

Multiply the terms

3 x^{3} \times 12 x

Multiply the terms

36 x^{3} \times x

Multiply the terms with the same base by adding their exponents

36 x^{3 + 1}

Add the numbers

36 x^{4}

36 x^{4} - 36 = 0

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

36 x^{4} = 0 + 36

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

36 x^{4} = 36

Divide both sides

\frac{36 x ^{4}}{36} = \frac{36}{36}

Divide the numbers

x^{4} = \frac{36}{36}

Divide the numbers

More Steps

Evaluate

\frac{36}{36}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{4} = 1

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 41

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

Solution

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

Show Solution