Solve 7p-5p-5p^3p 7p^2p

Question

Simplify the expression

2 p - 35 p^{7}

Evaluate

7 p - 5 p - 5 p^{3} \times p \times 7 p^{2} \times p

Multiply

More Steps

Multiply the terms

- 5 p^{3} \times p \times 7 p^{2} \times p

Multiply the terms

- 35 p^{3} \times p \times p^{2} \times p

Multiply the terms with the same base by adding their exponents

- 35 p^{3 + 1 + 2 + 1}

Add the numbers

- 35 p^{7}

7 p - 5 p - 35 p^{7}

Solution

More Steps

Evaluate

7 p - 5 p

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

(7 - 5) p

Subtract the numbers

2 p

2 p - 35 p^{7}

Show Solution

Factor the expression

p (2 - 35 p^{6})

Evaluate

7 p - 5 p - 5 p^{3} \times p \times 7 p^{2} \times p

Multiply

More Steps

Multiply the terms

5 p^{3} \times p \times 7 p^{2} \times p

Multiply the terms

35 p^{3} \times p \times p^{2} \times p

Multiply the terms with the same base by adding their exponents

35 p^{3 + 1 + 2 + 1}

Add the numbers

35 p^{7}

7 p - 5 p - 35 p^{7}

Subtract the terms

More Steps

Simplify

7 p - 5 p

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

(7 - 5) p

Subtract the numbers

2 p

2 p - 35 p^{7}

Rewrite the expression

p \times 2 - p \times 35 p^{6}

Solution

p (2 - 35 p^{6})

Show Solution

Find the roots

p_{1} = - \frac{6 2 \times 3 5 ^{5}}{35}, p_{2} = 0, p_{3} = \frac{6 2 \times 3 5 ^{5}}{35}

Alternative Form

p_{1} \approx - 0.620622, p_{2} = 0, p_{3} \approx 0.620622

Evaluate

7 p - 5 p - 5 p^{3} \times p \times 7 p^{2} \times p

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

7 p - 5 p - 5 p^{3} \times p \times 7 p^{2} \times p = 0

Multiply

More Steps

Multiply the terms

5 p^{3} \times p \times 7 p^{2} \times p

Multiply the terms

35 p^{3} \times p \times p^{2} \times p

Multiply the terms with the same base by adding their exponents

35 p^{3 + 1 + 2 + 1}

Add the numbers

35 p^{7}

7 p - 5 p - 35 p^{7} = 0

Subtract the terms

More Steps

Simplify

7 p - 5 p

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

(7 - 5) p

Subtract the numbers

2 p

2 p - 35 p^{7} = 0

Factor the expression

p (2 - 35 p^{6}) = 0

Separate the equation into 2 possible cases

p = 0 2 - 35 p^{6} = 0

Solve the equation

More Steps

Evaluate

2 - 35 p^{6} = 0

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

- 35 p^{6} = 0 - 2

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

- 35 p^{6} = - 2

Change the signs on both sides of the equation

35 p^{6} = 2

Divide both sides

\frac{35 p ^{6}}{35} = \frac{2}{35}

Divide the numbers

p^{6} = \frac{2}{35}

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

p = \pm 6 \frac{2}{35}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{35}

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

\frac{6 2}{6 35}

Multiply by the Conjugate

\frac{6 2 \times 6 3 5 ^{5}}{6 35 \times 6 3 5 ^{5}}

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

\frac{6 2 \times 3 5 ^{5}}{6 35 \times 6 3 5 ^{5}}

Multiply the numbers

\frac{6 2 \times 3 5 ^{5}}{35}

p = \pm \frac{6 2 \times 3 5 ^{5}}{35}

Separate the equation into 2 possible cases

p = \frac{6 2 \times 3 5 ^{5}}{35} p = - \frac{6 2 \times 3 5 ^{5}}{35}

p = 0 p = \frac{6 2 \times 3 5 ^{5}}{35} p = - \frac{6 2 \times 3 5 ^{5}}{35}

Solution

p_{1} = - \frac{6 2 \times 3 5 ^{5}}{35}, p_{2} = 0, p_{3} = \frac{6 2 \times 3 5 ^{5}}{35}

Alternative Form

p_{1} \approx - 0.620622, p_{2} = 0, p_{3} \approx 0.620622

Show Solution