Solve (2p 7)(3p^24p - 3)

Question

Simplify the expression

168 p^{4} - 42 p

Evaluate

(2 p \times 7) (3 p^{2} \times 4 p - 3)

Remove the parentheses

2 p \times 7 (3 p^{2} \times 4 p - 3)

Multiply

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Multiply the terms

3 p^{2} \times 4 p

Multiply the terms

12 p^{2} \times p

Multiply the terms with the same base by adding their exponents

12 p^{2 + 1}

Add the numbers

12 p^{3}

2 p \times 7 (12 p^{3} - 3)

Multiply the terms

14 p (12 p^{3} - 3)

Apply the distributive property

14 p \times 12 p^{3} - 14 p \times 3

Multiply the terms

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Evaluate

14 p \times 12 p^{3}

Multiply the numbers

168 p \times p^{3}

Multiply the terms

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Evaluate

p \times p^{3}

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

p^{1 + 3}

Add the numbers

p^{4}

168 p^{4}

168 p^{4} - 14 p \times 3

Solution

168 p^{4} - 42 p

Show Solution

Factor the expression

42 p (4 p^{3} - 1)

Evaluate

(2 p \times 7) (3 p^{2} \times 4 p - 3)

Remove the parentheses

2 p \times 7 (3 p^{2} \times 4 p - 3)

Multiply

More Steps

Multiply the terms

3 p^{2} \times 4 p

Multiply the terms

12 p^{2} \times p

Multiply the terms with the same base by adding their exponents

12 p^{2 + 1}

Add the numbers

12 p^{3}

2 p \times 7 (12 p^{3} - 3)

Multiply the terms

14 p (12 p^{3} - 3)

Factor the expression

14 p \times 3 (4 p^{3} - 1)

Solution

42 p (4 p^{3} - 1)

Show Solution

Find the roots

p_{1} = 0, p_{2} = \frac{3 2}{2}

Alternative Form

p_{1} = 0, p_{2} \approx 0.629961

Evaluate

(2 p \times 7) (3 p^{2} \times 4 p - 3)

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

(2 p \times 7) (3 p^{2} \times 4 p - 3) = 0

Multiply the terms

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

Multiply

More Steps

Multiply the terms

3 p^{2} \times 4 p

Multiply the terms

12 p^{2} \times p

Multiply the terms with the same base by adding their exponents

12 p^{2 + 1}

Add the numbers

12 p^{3}

14 p (12 p^{3} - 3) = 0

Elimination the left coefficient

p (12 p^{3} - 3) = 0

Separate the equation into 2 possible cases

p = 0 12 p^{3} - 3 = 0

Solve the equation

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Evaluate

12 p^{3} - 3 = 0

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

12 p^{3} = 0 + 3

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

12 p^{3} = 3

Divide both sides

\frac{12 p ^{3}}{12} = \frac{3}{12}

Divide the numbers

p^{3} = \frac{3}{12}

Cancel out the common factor 3

p^{3} = \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 p^{3} = 3 \frac{1}{4}

Calculate

p = 3 \frac{1}{4}

Simplify the root

More Steps

Evaluate

3 \frac{1}{4}

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

\frac{3 1}{3 4}

Simplify the radical expression

\frac{1}{3 4}

Multiply by the Conjugate

\frac{3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 2}{2 ^{2}}

Reduce the fraction

\frac{3 2}{2}

p = \frac{3 2}{2}

p = 0 p = \frac{3 2}{2}

Solution

p_{1} = 0, p_{2} = \frac{3 2}{2}

Alternative Form

p_{1} = 0, p_{2} \approx 0.629961

Show Solution