Solve (2x-1)(4x^2 2x 1)-7(x^3 1)

Question

Simplify the expression

16 x^{4} - 15 x^{3}

Evaluate

(2 x - 1) (4 x^{2} \times 2 x \times 1) - 7 (x^{3} \times 1)

Remove the parentheses

(2 x - 1) \times 4 x^{2} \times 2 x \times 1 - 7 x^{3} \times 1

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

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

Multiply the terms

(2 x - 1) \times 8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

(2 x - 1) \times 8 x^{2 + 1}

Add the numbers

(2 x - 1) \times 8 x^{3}

Multiply the terms

8 x^{3} (2 x - 1)

8 x^{3} (2 x - 1) - 7 x^{3} \times 1

Multiply the terms

8 x^{3} (2 x - 1) - 7 x^{3}

Expand the expression

More Steps

Calculate

8 x^{3} (2 x - 1)

Apply the distributive property

8 x^{3} \times 2 x - 8 x^{3} \times 1

Multiply the terms

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Evaluate

8 x^{3} \times 2 x

Multiply the numbers

16 x^{3} \times x

Multiply the terms

16 x^{4}

16 x^{4} - 8 x^{3} \times 1

Any expression multiplied by 1 remains the same

16 x^{4} - 8 x^{3}

16 x^{4} - 8 x^{3} - 7 x^{3}

Solution

More Steps

Evaluate

- 8 x^{3} - 7 x^{3}

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

(- 8 - 7) x^{3}

Subtract the numbers

- 15 x^{3}

16 x^{4} - 15 x^{3}

Show Solution

Factor the expression

(16 x - 15) x^{3}

Evaluate

(2 x - 1) (4 x^{2} \times 2 x \times 1) - 7 (x^{3} \times 1)

Remove the parentheses

(2 x - 1) \times 4 x^{2} \times 2 x \times 1 - 7 x^{3} \times 1

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

4 x^{2} \times 2 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

(2 x - 1) \times 8 x^{3} - 7 x^{3} \times 1

Multiply the terms

8 x^{3} (2 x - 1) - 7 x^{3} \times 1

Any expression multiplied by 1 remains the same

8 x^{3} (2 x - 1) - 7 x^{3}

Rewrite the expression

8 (2 x - 1) x^{3} - 7 x^{3}

Factor out x^{3} from the expression

(8 (2 x - 1) - 7) x^{3}

Solution

(16 x - 15) x^{3}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{15}{16}

Alternative Form

x_{1} = 0, x_{2} = 0.9375

Evaluate

(2 x - 1) (4 x^{2} \times 2 x \times 1) - 7 (x^{3} \times 1)

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

(2 x - 1) (4 x^{2} \times 2 x \times 1) - 7 (x^{3} \times 1) = 0

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

4 x^{2} \times 2 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

(2 x - 1) \times 8 x^{3} - 7 (x^{3} \times 1) = 0

Any expression multiplied by 1 remains the same

(2 x - 1) \times 8 x^{3} - 7 x^{3} = 0

Multiply the terms

8 x^{3} (2 x - 1) - 7 x^{3} = 0

Calculate

More Steps

Evaluate

8 x^{3} (2 x - 1) - 7 x^{3}

Expand the expression

More Steps

Calculate

8 x^{3} (2 x - 1)

Apply the distributive property

8 x^{3} \times 2 x - 8 x^{3} \times 1

Multiply the terms

16 x^{4} - 8 x^{3} \times 1

Any expression multiplied by 1 remains the same

16 x^{4} - 8 x^{3}

16 x^{4} - 8 x^{3} - 7 x^{3}

Subtract the terms

More Steps

Evaluate

- 8 x^{3} - 7 x^{3}

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

(- 8 - 7) x^{3}

Subtract the numbers

- 15 x^{3}

16 x^{4} - 15 x^{3}

16 x^{4} - 15 x^{3} = 0

Factor the expression

x^{3} (16 x - 15) = 0

Separate the equation into 2 possible cases

x^{3} = 0 16 x - 15 = 0

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

x = 0 16 x - 15 = 0

Solve the equation

More Steps

Evaluate

16 x - 15 = 0

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

16 x = 0 + 15

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

16 x = 15

Divide both sides

\frac{16 x}{16} = \frac{15}{16}

Divide the numbers

x = \frac{15}{16}

x = 0 x = \frac{15}{16}

Solution

x_{1} = 0, x_{2} = \frac{15}{16}

Alternative Form

x_{1} = 0, x_{2} = 0.9375

Show Solution