Solve 4a^3a - 26 - ScanMath

Question

Simplify the expression

4 a^{4} - 26

Evaluate

4 a^{3} \times a - 26

Solution

More Steps

Evaluate

4 a^{3} \times a

Multiply the terms with the same base by adding their exponents

4 a^{3 + 1}

Add the numbers

4 a^{4}

4 a^{4} - 26

Show Solution

Factor the expression

2 (2 a^{4} - 13)

Evaluate

4 a^{3} \times a - 26

Multiply

More Steps

Evaluate

4 a^{3} \times a

Multiply the terms with the same base by adding their exponents

4 a^{3 + 1}

Add the numbers

4 a^{4}

4 a^{4} - 26

Solution

2 (2 a^{4} - 13)

Show Solution

Find the roots

a_{1} = - \frac{4 104}{2}, a_{2} = \frac{4 104}{2}

Alternative Form

a_{1} \approx - 1.596718, a_{2} \approx 1.596718

Evaluate

4 a^{3} \times a - 26

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

4 a^{3} \times a - 26 = 0

Multiply

More Steps

Multiply the terms

4 a^{3} \times a

Multiply the terms with the same base by adding their exponents

4 a^{3 + 1}

Add the numbers

4 a^{4}

4 a^{4} - 26 = 0

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

4 a^{4} = 0 + 26

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

4 a^{4} = 26

Divide both sides

\frac{4 a ^{4}}{4} = \frac{26}{4}

Divide the numbers

a^{4} = \frac{26}{4}

Cancel out the common factor 2

a^{4} = \frac{13}{2}

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

a = \pm 4 \frac{13}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{13}{2}

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

\frac{4 13}{4 2}

Multiply by the Conjugate

\frac{4 13 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 13 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

413 \times 48

The product of roots with the same index is equal to the root of the product

4 13 \times 8

Calculate the product

4104

\frac{4 104}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

The product of roots with the same index is equal to the root of the product

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 104}{2}

a = \pm \frac{4 104}{2}

Separate the equation into 2 possible cases

a = \frac{4 104}{2} a = - \frac{4 104}{2}

Solution

a_{1} = - \frac{4 104}{2}, a_{2} = \frac{4 104}{2}

Alternative Form

a_{1} \approx - 1.596718, a_{2} \approx 1.596718

Show Solution