Solve (3x^5)2 - (2x -1)2

Question

Simplify the expression

6 x^{5} - 4 x + 2

Evaluate

3 x^{5} \times 2 - (2 x - 1) \times 2

Multiply the numbers

6 x^{5} - (2 x - 1) \times 2

Multiply the terms

6 x^{5} - 2 (2 x - 1)

Solution

More Steps

Evaluate

- 2 (2 x - 1)

Apply the distributive property

- 2 \times 2 x - (- 2 \times 1)

Multiply the numbers

- 4 x - (- 2 \times 1)

Any expression multiplied by 1 remains the same

- 4 x - (- 2)

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 + 2

6 x^{5} - 4 x + 2

Show Solution

Factor the expression

2 (x + 1) (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1)

Evaluate

3 x^{5} \times 2 - (2 x - 1) \times 2

Multiply the numbers

More Steps

Evaluate

3 \times 2

Multiply the numbers

6

Evaluate

6 x^{5}

6 x^{5} - (2 x - 1) \times 2

Multiply the terms

6 x^{5} - 2 (2 x - 1)

Simplify

More Steps

Evaluate

- 2 (2 x - 1)

Apply the distributive property

- 2 \times 2 x - 2 (- 1)

Multiply the terms

- 4 x - 2 (- 1)

Multiply the terms

- 4 x + 2

6 x^{5} - 4 x + 2

Rewrite the expression

2 \times 3 x^{5} - 2 \times 2 x + 2

Factor out 2 from the expression

2 (3 x^{5} - 2 x + 1)

Solution

More Steps

Evaluate

3 x^{5} - 2 x + 1

Calculate

3 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + x + 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1

Rewrite the expression

x \times 3 x^{4} - x \times 3 x^{3} + x \times 3 x^{2} - x \times 3 x + x + 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1

Factor out x from the expression

x (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1) + 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1

Factor out 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1 from the expression

(x + 1) (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1)

2 (x + 1) (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1)

Show Solution

Find the roots

x = - 1

Evaluate

(3 x^{5}) \times 2 - (2 x - 1) \times 2

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

(3 x^{5}) \times 2 - (2 x - 1) \times 2 = 0

Multiply the terms

3 x^{5} \times 2 - (2 x - 1) \times 2 = 0

Multiply the numbers

6 x^{5} - (2 x - 1) \times 2 = 0

Multiply the terms

6 x^{5} - 2 (2 x - 1) = 0

Calculate

More Steps

Evaluate

- 2 (2 x - 1)

Apply the distributive property

- 2 \times 2 x - (- 2 \times 1)

Multiply the numbers

- 4 x - (- 2 \times 1)

Any expression multiplied by 1 remains the same

- 4 x - (- 2)

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 + 2

6 x^{5} - 4 x + 2 = 0

Factor the expression

2 (x + 1) (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1) = 0

Divide both sides

(x + 1) (3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1) = 0

Separate the equation into 2 possible cases

x + 1 = 0 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1 = 0

Solve the equation

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 = - 1 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1 = 0

Solve the equation

x = - 1 x \in / R

Solution

x = - 1

Show Solution