Solve 4a-3a-4a^6a

Question

Simplify the expression

a - 4 a^{7}

Evaluate

4 a - 3 a - 4 a^{6} \times a

Multiply

More Steps

Multiply the terms

- 4 a^{6} \times a

Multiply the terms with the same base by adding their exponents

- 4 a^{6 + 1}

Add the numbers

- 4 a^{7}

4 a - 3 a - 4 a^{7}

Solution

More Steps

Evaluate

4 a - 3 a

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

(4 - 3) a

Subtract the numbers

a

a - 4 a^{7}

Show Solution

Factor the expression

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

Evaluate

4 a - 3 a - 4 a^{6} \times a

Multiply

More Steps

Multiply the terms

4 a^{6} \times a

Multiply the terms with the same base by adding their exponents

4 a^{6 + 1}

Add the numbers

4 a^{7}

4 a - 3 a - 4 a^{7}

Subtract the terms

More Steps

Simplify

4 a - 3 a

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

(4 - 3) a

Subtract the numbers

a

a - 4 a^{7}

Rewrite the expression

a - a \times 4 a^{6}

Factor out a from the expression

a (1 - 4 a^{6})

Solution

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

Show Solution

Find the roots

a_{1} = - \frac{3 4}{2}, a_{2} = 0, a_{3} = \frac{3 4}{2}

Alternative Form

a_{1} \approx - 0.793701, a_{2} = 0, a_{3} \approx 0.793701

Evaluate

4 a - 3 a - 4 a^{6} \times a

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

4 a - 3 a - 4 a^{6} \times a = 0

Multiply

More Steps

Multiply the terms

4 a^{6} \times a

Multiply the terms with the same base by adding their exponents

4 a^{6 + 1}

Add the numbers

4 a^{7}

4 a - 3 a - 4 a^{7} = 0

Subtract the terms

More Steps

Simplify

4 a - 3 a

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

(4 - 3) a

Subtract the numbers

a

a - 4 a^{7} = 0

Factor the expression

a (1 - 4 a^{6}) = 0

Separate the equation into 2 possible cases

a = 0 1 - 4 a^{6} = 0

Solve the equation

More Steps

Evaluate

1 - 4 a^{6} = 0

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

- 4 a^{6} = 0 - 1

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

- 4 a^{6} = - 1

Change the signs on both sides of the equation

4 a^{6} = 1

Divide both sides

\frac{4 a ^{6}}{4} = \frac{1}{4}

Divide the numbers

a^{6} = \frac{1}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 6 \frac{1}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{4}

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

\frac{6 1}{6 4}

Simplify the radical expression

\frac{1}{6 4}

Simplify the radical expression

\frac{1}{3 2}

Multiply by the Conjugate

\frac{3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 4}{2}

a = \pm \frac{3 4}{2}

Separate the equation into 2 possible cases

a = \frac{3 4}{2} a = - \frac{3 4}{2}

a = 0 a = \frac{3 4}{2} a = - \frac{3 4}{2}

Solution

a_{1} = - \frac{3 4}{2}, a_{2} = 0, a_{3} = \frac{3 4}{2}

Alternative Form

a_{1} \approx - 0.793701, a_{2} = 0, a_{3} \approx 0.793701

Show Solution