Solve (5n^2 2n)-(n^2-3n^6)

Question

Simplify the expression

10 n^{3} - n^{2} + 3 n^{6}

Evaluate

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

Multiply

More Steps

Multiply the terms

5 n^{2} \times 2 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - (n^{2} - 3 n^{6})

Solution

10 n^{3} - n^{2} + 3 n^{6}

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Factor the expression

n^{2} (10 n - 1 + 3 n^{4})

Evaluate

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

Multiply

More Steps

Multiply the terms

5 n^{2} \times 2 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - (n^{2} - 3 n^{6})

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

10 n^{3} - n^{2} + 3 n^{6}

Rewrite the expression

n^{2} \times 10 n - n^{2} + n^{2} \times 3 n^{4}

Solution

n^{2} (10 n - 1 + 3 n^{4})

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Find the roots

n_{1} \approx - 1.525749, n_{2} = 0, n_{3} \approx 0.09997

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

5 n^{2} \times 2 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - (n^{2} - 3 n^{6}) = 0

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

10 n^{3} - n^{2} + 3 n^{6} = 0

Factor the expression

n^{2} (10 n - 1 + 3 n^{4}) = 0

Separate the equation into 2 possible cases

n^{2} = 0 10 n - 1 + 3 n^{4} = 0

The only way a power can be 0 is when the base equals 0

n = 0 10 n - 1 + 3 n^{4} = 0

Solve the equation

n = 0 n \approx 0.09997 n \approx - 1.525749

Solution

n_{1} \approx - 1.525749, n_{2} = 0, n_{3} \approx 0.09997

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