Solve 1 - 3p 9p^2

Question

Simplify the expression

1 - 27 p^{3}

Evaluate

1 - 3 p \times 9 p^{2}

Solution

More Steps

Evaluate

3 p \times 9 p^{2}

Multiply the terms

27 p \times p^{2}

Multiply the terms with the same base by adding their exponents

27 p^{1 + 2}

Add the numbers

27 p^{3}

1 - 27 p^{3}

Show Solution

Factor the expression

(1 - 3 p) (1 + 3 p + 9 p^{2})

Evaluate

1 - 3 p \times 9 p^{2}

Evaluate

More Steps

Evaluate

3 p \times 9 p^{2}

Multiply the terms

27 p \times p^{2}

Multiply the terms with the same base by adding their exponents

27 p^{1 + 2}

Add the numbers

27 p^{3}

1 - 27 p^{3}

Rewrite the expression in exponential form

1^{3} - (3 p)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(1 - 3 p) (1^{2} + 1 \times 3 p + (3 p)^{2})

1 raised to any power equals to 1

(1 - 3 p) (1 + 1 \times 3 p + (3 p)^{2})

Any expression multiplied by 1 remains the same

(1 - 3 p) (1 + 3 p + (3 p)^{2})

Solution

More Steps

Evaluate

(3 p)^{2}

To raise a product to a power,raise each factor to that power

3^{2} p^{2}

Evaluate the power

9 p^{2}

(1 - 3 p) (1 + 3 p + 9 p^{2})

Show Solution

Find the roots

p = \frac{1}{3}

Alternative Form

p = 0. \dot{3}

Evaluate

1 - 3 p \times 9 p^{2}

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

1 - 3 p \times 9 p^{2} = 0

Multiply

More Steps

Multiply the terms

3 p \times 9 p^{2}

Multiply the terms

27 p \times p^{2}

Multiply the terms with the same base by adding their exponents

27 p^{1 + 2}

Add the numbers

27 p^{3}

1 - 27 p^{3} = 0

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

- 27 p^{3} = 0 - 1

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

- 27 p^{3} = - 1

Change the signs on both sides of the equation

27 p^{3} = 1

Divide both sides

\frac{27 p ^{3}}{27} = \frac{1}{27}

Divide the numbers

p^{3} = \frac{1}{27}

Take the 3 -th root on both sides of the equation

3 p^{3} = 3 \frac{1}{27}

Calculate

p = 3 \frac{1}{27}

Solution

More Steps

Evaluate

3 \frac{1}{27}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 27}

Simplify the radical expression

\frac{1}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{1}{3}

p = \frac{1}{3}

Alternative Form

p = 0. \dot{3}

Show Solution