Solve (12a^5 -6a-10a^3 )-(10a-2a^5 -14a^4 )

Question

Simplify the expression

14 a^{5} - 16 a - 10 a^{3} + 14 a^{4}

Evaluate

(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4})

Remove the parentheses

12 a^{5} - 6 a - 10 a^{3} - (10 a - 2 a^{5} - 14 a^{4})

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

12 a^{5} - 6 a - 10 a^{3} - 10 a + 2 a^{5} + 14 a^{4}

Add the terms

More Steps

Evaluate

12 a^{5} + 2 a^{5}

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

(12 + 2) a^{5}

Add the numbers

14 a^{5}

14 a^{5} - 6 a - 10 a^{3} - 10 a + 14 a^{4}

Solution

More Steps

Evaluate

- 6 a - 10 a

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

(- 6 - 10) a

Subtract the numbers

- 16 a

14 a^{5} - 16 a - 10 a^{3} + 14 a^{4}

Show Solution

Factor the expression

2 a (7 a^{4} - 8 - 5 a^{2} + 7 a^{3})

Evaluate

(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4})

Remove the parentheses

12 a^{5} - 6 a - 10 a^{3} - (10 a - 2 a^{5} - 14 a^{4})

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

12 a^{5} - 6 a - 10 a^{3} - 10 a + 2 a^{5} + 14 a^{4}

Add the terms

More Steps

Evaluate

12 a^{5} + 2 a^{5}

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

(12 + 2) a^{5}

Add the numbers

14 a^{5}

14 a^{5} - 6 a - 10 a^{3} - 10 a + 14 a^{4}

Subtract the terms

More Steps

Evaluate

- 6 a - 10 a

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

(- 6 - 10) a

Subtract the numbers

- 16 a

14 a^{5} - 16 a - 10 a^{3} + 14 a^{4}

Rewrite the expression

2 a \times 7 a^{4} - 2 a \times 8 - 2 a \times 5 a^{2} + 2 a \times 7 a^{3}

Solution

2 a (7 a^{4} - 8 - 5 a^{2} + 7 a^{3})

Show Solution

Find the roots

a_{1} \approx - 1.671827, a_{2} = 0, a_{3} \approx 0.973317

Evaluate

(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4})

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

(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4}) = 0

Remove the parentheses

12 a^{5} - 6 a - 10 a^{3} - (10 a - 2 a^{5} - 14 a^{4}) = 0

Subtract the terms

More Steps

Simplify

12 a^{5} - 6 a - 10 a^{3} - (10 a - 2 a^{5} - 14 a^{4})

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

12 a^{5} - 6 a - 10 a^{3} - 10 a + 2 a^{5} + 14 a^{4}

Add the terms

More Steps

Evaluate

12 a^{5} + 2 a^{5}

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

(12 + 2) a^{5}

Add the numbers

14 a^{5}

14 a^{5} - 6 a - 10 a^{3} - 10 a + 14 a^{4}

Subtract the terms

More Steps

Evaluate

- 6 a - 10 a

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

(- 6 - 10) a

Subtract the numbers

- 16 a

14 a^{5} - 16 a - 10 a^{3} + 14 a^{4}

14 a^{5} - 16 a - 10 a^{3} + 14 a^{4} = 0

Factor the expression

2 a (7 a^{4} - 8 - 5 a^{2} + 7 a^{3}) = 0

Divide both sides

a (7 a^{4} - 8 - 5 a^{2} + 7 a^{3}) = 0

Separate the equation into 2 possible cases

a = 0 7 a^{4} - 8 - 5 a^{2} + 7 a^{3} = 0

Solve the equation

a = 0 a \approx 0.973317 a \approx - 1.671827

Solution

a_{1} \approx - 1.671827, a_{2} = 0, a_{3} \approx 0.973317

Show Solution