Solve (5p^(2)-3) (2p^(^(^(2)))-3p)^(3)

Question

Simplify the expression

20 p^{3} - 21 p

Evaluate

(5 p^{2} - 3) (2 p \times 2) - 3 p \times 3

Remove the parentheses

(5 p^{2} - 3) \times 2 p \times 2 - 3 p \times 3

Multiply the terms

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Multiply the terms

(5 p^{2} - 3) \times 2 p \times 2

Multiply the terms

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

Multiply the terms

4 p (5 p^{2} - 3)

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

Multiply the terms

4 p (5 p^{2} - 3) - 9 p

Expand the expression

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Calculate

4 p (5 p^{2} - 3)

Apply the distributive property

4 p \times 5 p^{2} - 4 p \times 3

Multiply the terms

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Evaluate

4 p \times 5 p^{2}

Multiply the numbers

20 p \times p^{2}

Multiply the terms

20 p^{3}

20 p^{3} - 4 p \times 3

Multiply the numbers

20 p^{3} - 12 p

20 p^{3} - 12 p - 9 p

Solution

More Steps

Evaluate

- 12 p - 9 p

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

(- 12 - 9) p

Subtract the numbers

- 21 p

20 p^{3} - 21 p

Show Solution

Factor the expression

(20 p^{2} - 21) p

Evaluate

(5 p^{2} - 3) (2 p \times 2) - 3 p \times 3

Remove the parentheses

(5 p^{2} - 3) \times 2 p \times 2 - 3 p \times 3

Multiply the terms

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

Multiply the terms

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

Multiply the terms

4 p (5 p^{2} - 3) - 9 p

Rewrite the expression

4 (5 p^{2} - 3) p - 9 p

Factor out p from the expression

(4 (5 p^{2} - 3) - 9) p

Solution

(20 p^{2} - 21) p

Show Solution

Find the roots

p_{1} = - \frac{105}{10}, p_{2} = 0, p_{3} = \frac{105}{10}

Alternative Form

p_{1} \approx - 1.024695, p_{2} = 0, p_{3} \approx 1.024695

Evaluate

(5 p^{2} - 3) (2 p \times 2) - 3 p \times 3

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

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

4 p (5 p^{2} - 3) - 9 p = 0

Calculate

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Evaluate

4 p (5 p^{2} - 3) - 9 p

Expand the expression

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Calculate

4 p (5 p^{2} - 3)

Apply the distributive property

4 p \times 5 p^{2} - 4 p \times 3

Multiply the terms

20 p^{3} - 4 p \times 3

Multiply the numbers

20 p^{3} - 12 p

20 p^{3} - 12 p - 9 p

Subtract the terms

More Steps

Evaluate

- 12 p - 9 p

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

(- 12 - 9) p

Subtract the numbers

- 21 p

20 p^{3} - 21 p

20 p^{3} - 21 p = 0

Factor the expression

p (20 p^{2} - 21) = 0

Separate the equation into 2 possible cases

p = 0 20 p^{2} - 21 = 0

Solve the equation

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Evaluate

20 p^{2} - 21 = 0

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

20 p^{2} = 0 + 21

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

20 p^{2} = 21

Divide both sides

\frac{20 p ^{2}}{20} = \frac{21}{20}

Divide the numbers

p^{2} = \frac{21}{20}

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

p = \pm \frac{21}{20}

Simplify the expression

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Evaluate

\frac{21}{20}

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

\frac{21}{20}

Simplify the radical expression

\frac{21}{2 5}

Multiply by the Conjugate

\frac{21 \times 5}{2 5 \times 5}

Multiply the numbers

\frac{105}{2 5 \times 5}

Multiply the numbers

\frac{105}{10}

p = \pm \frac{105}{10}

Separate the equation into 2 possible cases

p = \frac{105}{10} p = - \frac{105}{10}

p = 0 p = \frac{105}{10} p = - \frac{105}{10}

Solution

p_{1} = - \frac{105}{10}, p_{2} = 0, p_{3} = \frac{105}{10}

Alternative Form

p_{1} \approx - 1.024695, p_{2} = 0, p_{3} \approx 1.024695

Show Solution