Solve (x^2-4)(x^2 6x 9)

Question

Simplify the expression

54 x^{5} - 216 x^{3}

Evaluate

(x^{2} - 4) (x^{2} \times 6 x \times 9)

Remove the parentheses

(x^{2} - 4) x^{2} \times 6 x \times 9

Multiply the terms with the same base by adding their exponents

(x^{2} - 4) x^{2 + 1} \times 6 \times 9

Add the numbers

(x^{2} - 4) x^{3} \times 6 \times 9

Multiply the terms

(x^{2} - 4) x^{3} \times 54

Use the commutative property to reorder the terms

(x^{2} - 4) \times 54 x^{3}

Multiply the terms

54 x^{3} (x^{2} - 4)

Apply the distributive property

54 x^{3} \times x^{2} - 54 x^{3} \times 4

Multiply the terms

More Steps

Evaluate

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

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

x^{3 + 2}

Add the numbers

x^{5}

54 x^{5} - 54 x^{3} \times 4

Solution

54 x^{5} - 216 x^{3}

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Factor the expression

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

Evaluate

(x^{2} - 4) (x^{2} \times 6 x \times 9)

Remove the parentheses

(x^{2} - 4) x^{2} \times 6 x \times 9

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x \times 9

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6 \times 9

Add the numbers

x^{3} \times 6 \times 9

Multiply the terms

x^{3} \times 54

Use the commutative property to reorder the terms

54 x^{3}

(x^{2} - 4) \times 54 x^{3}

Multiply the terms

54 x^{3} (x^{2} - 4)

Solution

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

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Find the roots

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

Evaluate

(x^{2} - 4) (x^{2} \times 6 x \times 9)

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

(x^{2} - 4) (x^{2} \times 6 x \times 9) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x \times 9

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6 \times 9

Add the numbers

x^{3} \times 6 \times 9

Multiply the terms

x^{3} \times 54

Use the commutative property to reorder the terms

54 x^{3}

(x^{2} - 4) \times 54 x^{3} = 0

Multiply the terms

54 x^{3} (x^{2} - 4) = 0

Elimination the left coefficient

x^{3} (x^{2} - 4) = 0

Separate the equation into 2 possible cases

x^{3} = 0 x^{2} - 4 = 0

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

x = 0 x^{2} - 4 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 4 = 0

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

x^{2} = 0 + 4

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

x^{2} = 4

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

x = \pm 4

Simplify the expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

x = 0 x = 2 x = - 2

Solution

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

Show Solution