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

Question

Simplify the expression

x^{8} - 6 x^{7} + 8 x^{6}

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x - 4) (x - 2) x^{6}

Multiply the terms

More Steps

Evaluate

(x - 4) (x - 2)

Apply the distributive property

x \times x - x \times 2 - 4 x - (- 4 \times 2)

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{2} - 2 x - 4 x - (- 8)

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^{2} - 2 x - 4 x + 8

Subtract the terms

More Steps

Evaluate

- 2 x - 4 x

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

(- 2 - 4) x

Subtract the numbers

- 6 x

x^{2} - 6 x + 8

(x^{2} - 6 x + 8) x^{6}

Apply the distributive property

x^{2} \times x^{6} - 6 x \times x^{6} + 8 x^{6}

Multiply the terms

More Steps

Evaluate

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

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

x^{2 + 6}

Add the numbers

x^{8}

x^{8} - 6 x \times x^{6} + 8 x^{6}

Solution

More Steps

Evaluate

x \times x^{6}

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

x^{1 + 6}

Add the numbers

x^{7}

x^{8} - 6 x^{7} + 8 x^{6}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 4

Evaluate

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

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

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

Calculate

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

Calculate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x - 4) (x - 2) x^{6}

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

Separate the equation into 3 possible cases

x - 4 = 0 x - 2 = 0 x^{6} = 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 = 0 x^{6} = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 4 x = 2 x^{6} = 0

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

x = 4 x = 2 x = 0

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 4

Show Solution