Solve (x^2-4)(x^2-1)

Question

Simplify the expression

x^{4} - 5 x^{2} + 4

Evaluate

(x^{2} - 4) (x^{2} - 1)

Apply the distributive property

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

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

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

Solution

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Evaluate

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

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

(- 1 - 4) x^{2}

Subtract the numbers

- 5 x^{2}

x^{4} - 5 x^{2} + 4

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Factor the expression

(x - 2) (x + 2) (x - 1) (x + 1)

Evaluate

(x^{2} - 4) (x^{2} - 1)

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

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

Solution

(x - 2) (x + 2) (x - 1) (x + 1)

Show Solution

Find the roots

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

Evaluate

(x^{2} - 4) (x^{2} - 1)

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

(x^{2} - 4) (x^{2} - 1) = 0

Separate the equation into 2 possible cases

x^{2} - 4 = 0 x^{2} - 1 = 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

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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} - 1 = 0

Solve the equation

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Evaluate

x^{2} - 1 = 0

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

x^{2} = 0 + 1

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

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

x = 2 x = - 2 x = 1 x = - 1

Solution

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

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