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

Question

Simplify the expression

16 x^{7} - 16 x^{6}

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x^{2} - x) x^{5} \times 4 \times 4

Multiply the terms

(x^{2} - x) x^{5} \times 16

Use the commutative property to reorder the terms

(x^{2} - x) \times 16 x^{5}

Multiply the terms

16 x^{5} (x^{2} - x)

Apply the distributive property

16 x^{5} \times x^{2} - 16 x^{5} \times x

Multiply the terms

More Steps

Evaluate

x^{5} \times x^{2}

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

x^{5 + 2}

Add the numbers

x^{7}

16 x^{7} - 16 x^{5} \times x

Solution

More Steps

Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

16 x^{7} - 16 x^{6}

Show Solution

Factor the expression

16 x^{6} (x - 1)

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

x^{2} \times 4 x \times 1

Rewrite the expression

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x^{2} - x) \times 16 x^{5}

Multiply the terms

16 x^{5} (x^{2} - x)

Factor the expression

More Steps

Evaluate

x^{2} - x

Rewrite the expression

x \times x - x

Factor out x from the expression

x (x - 1)

16 x^{5} \times x (x - 1)

Solution

16 x^{6} (x - 1)

Show Solution

Find the roots

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

Evaluate

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

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

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

x^{2} \times 4 x \times 1

Rewrite the expression

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

(x^{2} - x) \times 4 x^{3} \times 4 x^{2} = 0

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x^{2} - x) \times 16 x^{5}

Multiply the terms

16 x^{5} (x^{2} - x)

16 x^{5} (x^{2} - x) = 0

Elimination the left coefficient

x^{5} (x^{2} - x) = 0

Separate the equation into 2 possible cases

x^{5} = 0 x^{2} - x = 0

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

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

Solve the equation

More Steps

Evaluate

x^{2} - x = 0

Factor the expression

More Steps

Evaluate

x^{2} - x

Rewrite the expression

x \times x - x

Factor out x from the expression

x (x - 1)

x (x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1

x = 0 x = 0 x = 1

Find the union

x = 0 x = 1

Solution

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

Show Solution