Solve (-2k^3-7k^2 5k) (6k^2 3k)

Question

Simplify the expression

- 666 k^{6}

Evaluate

(- 2 k^{3} - 7 k^{2} \times 5 k) (6 k^{2} \times 3 k)

Remove the parentheses

(- 2 k^{3} - 7 k^{2} \times 5 k) \times 6 k^{2} \times 3 k

Multiply

More Steps

Multiply the terms

7 k^{2} \times 5 k

Multiply the terms

35 k^{2} \times k

Multiply the terms with the same base by adding their exponents

35 k^{2 + 1}

Add the numbers

35 k^{3}

(- 2 k^{3} - 35 k^{3}) \times 6 k^{2} \times 3 k

Subtract the terms

More Steps

Simplify

- 2 k^{3} - 35 k^{3}

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

(- 2 - 35) k^{3}

Subtract the numbers

- 37 k^{3}

(- 37 k^{3}) \times 6 k^{2} \times 3 k

Remove the parentheses

- 37 k^{3} \times 6 k^{2} \times 3 k

Multiply the terms

More Steps

Evaluate

37 \times 6 \times 3

Multiply the terms

222 \times 3

Multiply the numbers

666

- 666 k^{3} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

- 666 k^{3 + 2 + 1}

Solution

- 666 k^{6}

Show Solution

Find the roots

k = 0

Evaluate

(- 2 k^{3} - 7 k^{2} \times 5 k) (6 k^{2} \times 3 k)

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

(- 2 k^{3} - 7 k^{2} \times 5 k) (6 k^{2} \times 3 k) = 0

Multiply

More Steps

Multiply the terms

7 k^{2} \times 5 k

Multiply the terms

35 k^{2} \times k

Multiply the terms with the same base by adding their exponents

35 k^{2 + 1}

Add the numbers

35 k^{3}

(- 2 k^{3} - 35 k^{3}) (6 k^{2} \times 3 k) = 0

Subtract the terms

More Steps

Simplify

- 2 k^{3} - 35 k^{3}

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

(- 2 - 35) k^{3}

Subtract the numbers

- 37 k^{3}

(- 37 k^{3}) (6 k^{2} \times 3 k) = 0

Remove the parentheses

- 37 k^{3} (6 k^{2} \times 3 k) = 0

Multiply

More Steps

Multiply the terms

6 k^{2} \times 3 k

Multiply the terms

18 k^{2} \times k

Multiply the terms with the same base by adding their exponents

18 k^{2 + 1}

Add the numbers

18 k^{3}

- 37 k^{3} \times 18 k^{3} = 0

Multiply the terms

More Steps

Evaluate

- 37 k^{3} \times 18 k^{3}

Multiply the numbers

- 666 k^{3} \times k^{3}

Multiply the terms

More Steps

Evaluate

k^{3} \times k^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

k^{3 + 3}

Add the numbers

k^{6}

- 666 k^{6}

- 666 k^{6} = 0

Change the signs on both sides of the equation

666 k^{6} = 0

Rewrite the expression

k^{6} = 0

Solution

k = 0

Show Solution