Solve (5n^33n^2-2n)-(3n-7n^3-4n^2)

Question

Simplify the expression

15 n^{5} - 5 n + 7 n^{3} + 4 n^{2}

Evaluate

(5 n^{3} \times 3 n^{2} - 2 n) - (3 n - 7 n^{3} - 4 n^{2})

Multiply

More Steps

Multiply the terms

5 n^{3} \times 3 n^{2}

Multiply the terms

15 n^{3} \times n^{2}

Multiply the terms with the same base by adding their exponents

15 n^{3 + 2}

Add the numbers

15 n^{5}

(15 n^{5} - 2 n) - (3 n - 7 n^{3} - 4 n^{2})

Remove the parentheses

15 n^{5} - 2 n - (3 n - 7 n^{3} - 4 n^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

15 n^{5} - 2 n - 3 n + 7 n^{3} + 4 n^{2}

Solution

More Steps

Evaluate

- 2 n - 3 n

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

(- 2 - 3) n

Subtract the numbers

- 5 n

15 n^{5} - 5 n + 7 n^{3} + 4 n^{2}

Show Solution

Factor the expression

n (15 n^{4} - 5 + 7 n^{2} + 4 n)

Evaluate

(5 n^{3} \times 3 n^{2} - 2 n) - (3 n - 7 n^{3} - 4 n^{2})

Multiply

More Steps

Multiply the terms

5 n^{3} \times 3 n^{2}

Multiply the terms

15 n^{3} \times n^{2}

Multiply the terms with the same base by adding their exponents

15 n^{3 + 2}

Add the numbers

15 n^{5}

(15 n^{5} - 2 n) - (3 n - 7 n^{3} - 4 n^{2})

Remove the parentheses

15 n^{5} - 2 n - (3 n - 7 n^{3} - 4 n^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

15 n^{5} - 2 n - 3 n + 7 n^{3} + 4 n^{2}

Subtract the terms

More Steps

Evaluate

- 2 n - 3 n

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

(- 2 - 3) n

Subtract the numbers

- 5 n

15 n^{5} - 5 n + 7 n^{3} + 4 n^{2}

Rewrite the expression

n \times 15 n^{4} - n \times 5 + n \times 7 n^{2} + n \times 4 n

Solution

n (15 n^{4} - 5 + 7 n^{2} + 4 n)

Show Solution

Find the roots

n_{1} \approx - 0.72762, n_{2} = 0, n_{3} \approx 0.516453

Evaluate

(5 n^{3} \times 3 n^{2} - 2 n) - (3 n - 7 n^{3} - 4 n^{2})

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

(5 n^{3} \times 3 n^{2} - 2 n) - (3 n - 7 n^{3} - 4 n^{2}) = 0

Multiply

More Steps

Multiply the terms

5 n^{3} \times 3 n^{2}

Multiply the terms

15 n^{3} \times n^{2}

Multiply the terms with the same base by adding their exponents

15 n^{3 + 2}

Add the numbers

15 n^{5}

(15 n^{5} - 2 n) - (3 n - 7 n^{3} - 4 n^{2}) = 0

Remove the parentheses

15 n^{5} - 2 n - (3 n - 7 n^{3} - 4 n^{2}) = 0

Subtract the terms

More Steps

Simplify

15 n^{5} - 2 n - (3 n - 7 n^{3} - 4 n^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

15 n^{5} - 2 n - 3 n + 7 n^{3} + 4 n^{2}

Subtract the terms

More Steps

Evaluate

- 2 n - 3 n

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

(- 2 - 3) n

Subtract the numbers

- 5 n

15 n^{5} - 5 n + 7 n^{3} + 4 n^{2}

15 n^{5} - 5 n + 7 n^{3} + 4 n^{2} = 0

Factor the expression

n (15 n^{4} - 5 + 7 n^{2} + 4 n) = 0

Separate the equation into 2 possible cases

n = 0 15 n^{4} - 5 + 7 n^{2} + 4 n = 0

Solve the equation

n = 0 n \approx 0.516453 n \approx - 0.72762

Solution

n_{1} \approx - 0.72762, n_{2} = 0, n_{3} \approx 0.516453

Show Solution