Solve 1-125w^3 - ScanMath

Question

Factor the expression

(1 - 5 w) (1 + 5 w + 25 w^{2})

Evaluate

1 - 125 w^{3}

Rewrite the expression in exponential form

1^{3} - (5 w)^{3}

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

(1 - 5 w) (1^{2} + 1 \times 5 w + (5 w)^{2})

1 raised to any power equals to 1

(1 - 5 w) (1 + 1 \times 5 w + (5 w)^{2})

Any expression multiplied by 1 remains the same

(1 - 5 w) (1 + 5 w + (5 w)^{2})

Solution

More Steps

Evaluate

(5 w)^{2}

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

5^{2} w^{2}

Evaluate the power

25 w^{2}

(1 - 5 w) (1 + 5 w + 25 w^{2})

Show Solution

w = \frac{1}{5}

Alternative Form

w = 0.2

Evaluate

1 - 125 w^{3}

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

1 - 125 w^{3} = 0

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

- 125 w^{3} = 0 - 1

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

- 125 w^{3} = - 1

Change the signs on both sides of the equation

125 w^{3} = 1

Divide both sides

\frac{125 w ^{3}}{125} = \frac{1}{125}

Divide the numbers

w^{3} = \frac{1}{125}

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

3 w^{3} = 3 \frac{1}{125}

Calculate

w = 3 \frac{1}{125}

Solution

More Steps

Evaluate

3 \frac{1}{125}

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

\frac{3 1}{3 125}

Simplify the radical expression

\frac{1}{3 125}

Simplify the radical expression

More Steps

Evaluate

3125

Write the number in exponential form with the base of 5

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{1}{5}

w = \frac{1}{5}

Alternative Form

w = 0.2

Show Solution