Solve (x^2-1)(4x^2-25)

Question

Simplify the expression

4 x^{4} - 29 x^{2} + 25

Evaluate

(x^{2} - 1) (4 x^{2} - 25)

Apply the distributive property

x^{2} \times 4 x^{2} - x^{2} \times 25 - 4 x^{2} - (- 25)

Multiply the terms

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Evaluate

x^{2} \times 4 x^{2}

Use the commutative property to reorder the terms

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

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}

4 x^{4}

4 x^{4} - x^{2} \times 25 - 4 x^{2} - (- 25)

Use the commutative property to reorder the terms

4 x^{4} - 25 x^{2} - 4 x^{2} - (- 25)

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

4 x^{4} - 25 x^{2} - 4 x^{2} + 25

Solution

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Evaluate

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

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

(- 25 - 4) x^{2}

Subtract the numbers

- 29 x^{2}

4 x^{4} - 29 x^{2} + 25

Show Solution

Factor the expression

(x - 1) (x + 1) (2 x - 5) (2 x + 5)

Evaluate

(x^{2} - 1) (4 x^{2} - 25)

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

(x - 1) (x + 1) (4 x^{2} - 25)

Solution

(x - 1) (x + 1) (2 x - 5) (2 x + 5)

Show Solution

Find the roots

x_{1} = - \frac{5}{2}, x_{2} = - 1, x_{3} = 1, x_{4} = \frac{5}{2}

Alternative Form

x_{1} = - 2.5, x_{2} = - 1, x_{3} = 1, x_{4} = 2.5

Evaluate

(x^{2} - 1) (4 x^{2} - 25)

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

(x^{2} - 1) (4 x^{2} - 25) = 0

Separate the equation into 2 possible cases

x^{2} - 1 = 0 4 x^{2} - 25 = 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 = 1 x = - 1 4 x^{2} - 25 = 0

Solve the equation

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Evaluate

4 x^{2} - 25 = 0

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

4 x^{2} = 0 + 25

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

4 x^{2} = 25

Divide both sides

\frac{4 x ^{2}}{4} = \frac{25}{4}

Divide the numbers

x^{2} = \frac{25}{4}

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

x = \pm \frac{25}{4}

Simplify the expression

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Evaluate

\frac{25}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{25}{4}

Simplify the radical expression

\frac{5}{4}

Simplify the radical expression

\frac{5}{2}

x = \pm \frac{5}{2}

Separate the equation into 2 possible cases

x = \frac{5}{2} x = - \frac{5}{2}

x = 1 x = - 1 x = \frac{5}{2} x = - \frac{5}{2}

Solution

x_{1} = - \frac{5}{2}, x_{2} = - 1, x_{3} = 1, x_{4} = \frac{5}{2}

Alternative Form

x_{1} = - 2.5, x_{2} = - 1, x_{3} = 1, x_{4} = 2.5

Show Solution