Solve b^36b-20 - ScanMath

Question

Simplify the expression

6 b^{4} - 20

Evaluate

b^{3} \times 6 b - 20

Solution

More Steps

Evaluate

b^{3} \times 6 b

Multiply the terms with the same base by adding their exponents

b^{3 + 1} \times 6

Add the numbers

b^{4} \times 6

Use the commutative property to reorder the terms

6 b^{4}

6 b^{4} - 20

Show Solution

Factor the expression

2 (3 b^{4} - 10)

Evaluate

b^{3} \times 6 b - 20

Multiply

More Steps

Evaluate

b^{3} \times 6 b

Multiply the terms with the same base by adding their exponents

b^{3 + 1} \times 6

Add the numbers

b^{4} \times 6

Use the commutative property to reorder the terms

6 b^{4}

6 b^{4} - 20

Solution

2 (3 b^{4} - 10)

Show Solution

Find the roots

b_{1} = - \frac{4 270}{3}, b_{2} = \frac{4 270}{3}

Alternative Form

b_{1} \approx - 1.3512, b_{2} \approx 1.3512

Evaluate

b^{3} \times 6 b - 20

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

b^{3} \times 6 b - 20 = 0

Multiply

More Steps

Multiply the terms

b^{3} \times 6 b

Multiply the terms with the same base by adding their exponents

b^{3 + 1} \times 6

Add the numbers

b^{4} \times 6

Use the commutative property to reorder the terms

6 b^{4}

6 b^{4} - 20 = 0

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

6 b^{4} = 0 + 20

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

6 b^{4} = 20

Divide both sides

\frac{6 b ^{4}}{6} = \frac{20}{6}

Divide the numbers

b^{4} = \frac{20}{6}

Cancel out the common factor 2

b^{4} = \frac{10}{3}

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

b = \pm 4 \frac{10}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{10}{3}

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

\frac{4 10}{4 3}

Multiply by the Conjugate

\frac{4 10 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 10 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

410 \times 427

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

4 10 \times 27

Calculate the product

4270

\frac{4 270}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 270}{3}

b = \pm \frac{4 270}{3}

Separate the equation into 2 possible cases

b = \frac{4 270}{3} b = - \frac{4 270}{3}

Solution

b_{1} = - \frac{4 270}{3}, b_{2} = \frac{4 270}{3}

Alternative Form

b_{1} \approx - 1.3512, b_{2} \approx 1.3512

Show Solution