Solve -a^2 4a-4 - ScanMath

Question

Simplify the expression

- 4 a^{3} - 4

Evaluate

- a^{2} \times 4 a - 4

Solution

More Steps

Evaluate

- a^{2} \times 4 a

Multiply the terms with the same base by adding their exponents

- a^{2 + 1} \times 4

Add the numbers

- a^{3} \times 4

Use the commutative property to reorder the terms

- 4 a^{3}

- 4 a^{3} - 4

Show Solution

Factor the expression

- 4 (a + 1) (a^{2} - a + 1)

Evaluate

- a^{2} \times 4 a - 4

Evaluate

More Steps

Evaluate

a^{2} \times 4 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 4

Add the numbers

a^{3} \times 4

Use the commutative property to reorder the terms

4 a^{3}

- 4 a^{3} - 4

Factor out - 4 from the expression

- 4 (a^{3} + 1)

Solution

More Steps

Evaluate

a^{3} + 1

Rewrite the expression in exponential form

a^{3} + 1^{3}

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

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

Any expression multiplied by 1 remains the same

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

1 raised to any power equals to 1

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

- 4 (a + 1) (a^{2} - a + 1)

Show Solution

Find the roots

a = - 1

Evaluate

- a^{2} \times 4 a - 4

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

- a^{2} \times 4 a - 4 = 0

Multiply

More Steps

Multiply the terms

a^{2} \times 4 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 4

Add the numbers

a^{3} \times 4

Use the commutative property to reorder the terms

4 a^{3}

- 4 a^{3} - 4 = 0

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

- 4 a^{3} = 0 + 4

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

- 4 a^{3} = 4

Change the signs on both sides of the equation

4 a^{3} = - 4

Divide both sides

\frac{4 a ^{3}}{4} = \frac{- 4}{4}

Divide the numbers

a^{3} = \frac{- 4}{4}

Divide the numbers

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Evaluate

\frac{- 4}{4}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

a^{3} = - 1

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

3 a^{3} = 3 - 1

Calculate

a = 3 - 1

Solution

More Steps

Evaluate

3 - 1

An odd root of a negative radicand is always a negative

- 31

Simplify the radical expression

- 1

a = - 1

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