Solve r^22r-2 - ScanMath

Question

Simplify the expression

2 r^{3} - 2

Evaluate

r^{2} \times 2 r - 2

Solution

More Steps

Evaluate

r^{2} \times 2 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 2

Add the numbers

r^{3} \times 2

Use the commutative property to reorder the terms

2 r^{3}

2 r^{3} - 2

Show Solution

2 (r - 1) (r^{2} + r + 1)

Evaluate

r^{2} \times 2 r - 2

Evaluate

More Steps

Evaluate

r^{2} \times 2 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 2

Add the numbers

r^{3} \times 2

Use the commutative property to reorder the terms

2 r^{3}

2 r^{3} - 2

Factor out 2 from the expression

2 (r^{3} - 1)

Solution

More Steps

Evaluate

r^{3} - 1

Rewrite the expression in exponential form

r^{3} - 1^{3}

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

(r - 1) (r^{2} + r \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(r - 1) (r^{2} + r + 1^{2})

1 raised to any power equals to 1

(r - 1) (r^{2} + r + 1)

2 (r - 1) (r^{2} + r + 1)

Show Solution

r = 1

Evaluate

r^{2} \times 2 r - 2

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

r^{2} \times 2 r - 2 = 0

Multiply

More Steps

Multiply the terms

r^{2} \times 2 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 2

Add the numbers

r^{3} \times 2

Use the commutative property to reorder the terms

2 r^{3}

2 r^{3} - 2 = 0

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

2 r^{3} = 0 + 2

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

2 r^{3} = 2

Divide both sides

\frac{2 r ^{3}}{2} = \frac{2}{2}

Divide the numbers

r^{3} = \frac{2}{2}

Divide the numbers

More Steps

Evaluate

\frac{2}{2}

Reduce the numbers

\frac{1}{1}

Calculate

1

r^{3} = 1

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

3 r^{3} = 31

Calculate

r = 31

Solution

r = 1

Show Solution