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

Question

Simplify the expression

x^{4} - 13 x^{2} + 36

Evaluate

(x^{2} - 4) (x^{2} - 9)

Apply the distributive property

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

Multiply the terms

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Evaluate

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

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

x^{2 + 2}

Add the numbers

x^{4}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{4} - 9 x^{2} - 4 x^{2} - (- 36)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{4} - 9 x^{2} - 4 x^{2} + 36

Solution

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Evaluate

- 9 x^{2} - 4 x^{2}

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

(- 9 - 4) x^{2}

Subtract the numbers

- 13 x^{2}

x^{4} - 13 x^{2} + 36

Show Solution

Factor the expression

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

Evaluate

(x^{2} - 4) (x^{2} - 9)

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

(x - 2) (x + 2) (x^{2} - 9)

Solution

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

Show Solution

Find the roots

x_{1} = - 3, x_{2} = - 2, x_{3} = 2, x_{4} = 3

Evaluate

(x^{2} - 4) (x^{2} - 9)

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

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

Separate the equation into 2 possible cases

x^{2} - 4 = 0 x^{2} - 9 = 0

Solve the equation

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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

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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 = 2 x = - 2 x^{2} - 9 = 0

Solve the equation

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Evaluate

x^{2} - 9 = 0

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

x^{2} = 0 + 9

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

x^{2} = 9

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

x = \pm 9

Simplify the expression

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Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

x = 2 x = - 2 x = 3 x = - 3

Solution

x_{1} = - 3, x_{2} = - 2, x_{3} = 2, x_{4} = 3

Show Solution