Solve (x-4)(x^2 - 16)

Question

Simplify the expression

x^{3} - 16 x - 4 x^{2} + 64

Evaluate

(x - 4) (x^{2} - 16)

Apply the distributive property

x \times x^{2} - x \times 16 - 4 x^{2} - (- 4 \times 16)

Multiply the terms

More Steps

Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

x^{3} - x \times 16 - 4 x^{2} - (- 4 \times 16)

Use the commutative property to reorder the terms

x^{3} - 16 x - 4 x^{2} - (- 4 \times 16)

Multiply the numbers

x^{3} - 16 x - 4 x^{2} - (- 64)

Solution

x^{3} - 16 x - 4 x^{2} + 64

Show Solution

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

Evaluate

(x - 4) (x^{2} - 16)

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

(x - 4) (x - 4) (x + 4)

Solution

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

Show Solution

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

Evaluate

(x - 4) (x^{2} - 16)

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

(x - 4) (x^{2} - 16) = 0

Separate the equation into 2 possible cases

x - 4 = 0 x^{2} - 16 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 x^{2} - 16 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 16 = 0

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

x^{2} = 0 + 16

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

x^{2} = 16

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

x = \pm 16

Simplify the expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

x = \pm 4

Separate the equation into 2 possible cases

x = 4 x = - 4

x = 4 x = 4 x = - 4

Find the union

x = 4 x = - 4

Solution

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

Show Solution