Solve (-7p^6-9p^5 10p^3)(-9p^2 5)

Question

Simplify the expression

315 p^{8} + 4050 p^{10}

Evaluate

(- 7 p^{6} - 9 p^{5} \times 10 p^{3}) (- 9 p^{2} \times 5)

Rewrite the expression

(- 7 p^{6} - 9 p^{5} \times 10 p^{3}) (- 9) p^{2} \times 5

Multiply

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Multiply the terms

9 p^{5} \times 10 p^{3}

Multiply the terms

90 p^{5} \times p^{3}

Multiply the terms with the same base by adding their exponents

90 p^{5 + 3}

Add the numbers

90 p^{8}

(- 7 p^{6} - 90 p^{8}) (- 9) p^{2} \times 5

Rewrite the expression

- (- 7 p^{6} - 90 p^{8}) \times 9 p^{2} \times 5

Multiply the terms

- (- 7 p^{6} - 90 p^{8}) \times 45 p^{2}

Multiply the first two terms

(7 p^{6} + 90 p^{8}) \times 45 p^{2}

Multiply the terms

45 p^{2} (7 p^{6} + 90 p^{8})

Apply the distributive property

45 p^{2} \times 7 p^{6} + 45 p^{2} \times 90 p^{8}

Multiply the terms

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Evaluate

45 p^{2} \times 7 p^{6}

Multiply the numbers

315 p^{2} \times p^{6}

Multiply the terms

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Evaluate

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

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

p^{2 + 6}

Add the numbers

p^{8}

315 p^{8}

315 p^{8} + 45 p^{2} \times 90 p^{8}

Solution

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Evaluate

45 p^{2} \times 90 p^{8}

Multiply the numbers

4050 p^{2} \times p^{8}

Multiply the terms

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Evaluate

p^{2} \times p^{8}

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

p^{2 + 8}

Add the numbers

p^{10}

4050 p^{10}

315 p^{8} + 4050 p^{10}

Show Solution

Factor the expression

45 p^{8} (7 + 90 p^{2})

Evaluate

(- 7 p^{6} - 9 p^{5} \times 10 p^{3}) (- 9 p^{2} \times 5)

Multiply

More Steps

Multiply the terms

9 p^{5} \times 10 p^{3}

Multiply the terms

90 p^{5} \times p^{3}

Multiply the terms with the same base by adding their exponents

90 p^{5 + 3}

Add the numbers

90 p^{8}

(- 7 p^{6} - 90 p^{8}) (- 9 p^{2} \times 5)

Multiply the terms

(- 7 p^{6} - 90 p^{8}) (- 45 p^{2})

Multiply the terms

- 45 p^{2} (- 7 p^{6} - 90 p^{8})

Factor the expression

More Steps

Evaluate

- 7 p^{6} - 90 p^{8}

Rewrite the expression

- p^{6} \times 7 - p^{6} \times 90 p^{2}

Factor out - p^{6} from the expression

- p^{6} (7 + 90 p^{2})

- 45 p^{2} (- p^{6}) (7 + 90 p^{2})

Solution

45 p^{8} (7 + 90 p^{2})

Show Solution

Find the roots

p_{1} = - \frac{70}{30} i, p_{2} = \frac{70}{30} i, p_{3} = 0

Alternative Form

p_{1} \approx - 0.278887 i, p_{2} \approx 0.278887 i, p_{3} = 0

Evaluate

(- 7 p^{6} - 9 p^{5} \times 10 p^{3}) (- 9 p^{2} \times 5)

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

(- 7 p^{6} - 9 p^{5} \times 10 p^{3}) (- 9 p^{2} \times 5) = 0

Multiply

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Multiply the terms

9 p^{5} \times 10 p^{3}

Multiply the terms

90 p^{5} \times p^{3}

Multiply the terms with the same base by adding their exponents

90 p^{5 + 3}

Add the numbers

90 p^{8}

(- 7 p^{6} - 90 p^{8}) (- 9 p^{2} \times 5) = 0

Multiply the terms

(- 7 p^{6} - 90 p^{8}) (- 45 p^{2}) = 0

Multiply the terms

- 45 p^{2} (- 7 p^{6} - 90 p^{8}) = 0

Change the sign

45 p^{2} (- 7 p^{6} - 90 p^{8}) = 0

Elimination the left coefficient

p^{2} (- 7 p^{6} - 90 p^{8}) = 0

Separate the equation into 2 possible cases

p^{2} = 0 - 7 p^{6} - 90 p^{8} = 0

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

p = 0 - 7 p^{6} - 90 p^{8} = 0

Solve the equation

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Evaluate

- 7 p^{6} - 90 p^{8} = 0

Factor the expression

- p^{6} (7 + 90 p^{2}) = 0

Divide both sides

p^{6} (7 + 90 p^{2}) = 0

Separate the equation into 2 possible cases

p^{6} = 0 7 + 90 p^{2} = 0

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

p = 0 7 + 90 p^{2} = 0

Solve the equation

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Evaluate

7 + 90 p^{2} = 0

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

90 p^{2} = 0 - 7

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

90 p^{2} = - 7

Divide both sides

\frac{90 p ^{2}}{90} = \frac{- 7}{90}

Divide the numbers

p^{2} = \frac{- 7}{90}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

p^{2} = - \frac{7}{90}

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

p = \pm - \frac{7}{90}

Simplify the expression

p = \pm \frac{70}{30} i

Separate the equation into 2 possible cases

p = \frac{70}{30} i p = - \frac{70}{30} i

p = 0 p = \frac{70}{30} i p = - \frac{70}{30} i

p = 0 p = 0 p = \frac{70}{30} i p = - \frac{70}{30} i

Find the union

p = 0 p = \frac{70}{30} i p = - \frac{70}{30} i

Solution

p_{1} = - \frac{70}{30} i, p_{2} = \frac{70}{30} i, p_{3} = 0

Alternative Form

p_{1} \approx - 0.278887 i, p_{2} \approx 0.278887 i, p_{3} = 0

Show Solution