Solve (4p-1)(4p^2+4p+1)

Question

Simplify the expression

Solution

16 p^{3} + 12 p^{2} - 1

Evaluate

(4 p - 1) (4 p^{2} + 4 p + 1)

Apply the distributive property

4 p \times 4 p^{2} + 4 p \times 4 p + 4 p \times 1 - 4 p^{2} - 4 p - 1

Multiply the terms

More Steps

Evaluate

4 p \times 4 p^{2}

Multiply the numbers

16 p \times p^{2}

Multiply the terms

More Steps

Evaluate

p \times p^{2}

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

p^{1 + 2}

Add the numbers

p^{3}

16 p^{3}

16 p^{3} + 4 p \times 4 p + 4 p \times 1 - 4 p^{2} - 4 p - 1

Multiply the terms

More Steps

Evaluate

4 p \times 4 p

Multiply the numbers

16 p \times p

Multiply the terms

16 p^{2}

16 p^{3} + 16 p^{2} + 4 p \times 1 - 4 p^{2} - 4 p - 1

Any expression multiplied by 1 remains the same

16 p^{3} + 16 p^{2} + 4 p - 4 p^{2} - 4 p - 1

Subtract the terms

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Evaluate

16 p^{2} - 4 p^{2}

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

(16 - 4) p^{2}

Subtract the numbers

12 p^{2}

16 p^{3} + 12 p^{2} + 4 p - 4 p - 1

The sum of two opposites equals 0

More Steps

Evaluate

4 p - 4 p

Collect like terms

(4 - 4) p

Add the coefficients

0 \times p

Calculate

0

16 p^{3} + 12 p^{2} + 0 - 1

Solution

16 p^{3} + 12 p^{2} - 1

Show Solution

Factor the expression

Factor

(4 p - 1) (2 p + 1)^{2}

Evaluate

(4 p - 1) (4 p^{2} + 4 p + 1)

Solution

(4 p - 1) (2 p + 1)^{2}

Show Solution

Find the roots

Find the roots of the algebra expression

p_{1} = - \frac{1}{2}, p_{2} = \frac{1}{4}

Alternative Form

p_{1} = - 0.5, p_{2} = 0.25

Evaluate

(4 p - 1) (4 p^{2} + 4 p + 1)

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

(4 p - 1) (4 p^{2} + 4 p + 1) = 0

Separate the equation into 2 possible cases

4 p - 1 = 0 4 p^{2} + 4 p + 1 = 0

Solve the equation

More Steps

Evaluate

4 p - 1 = 0

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

4 p = 0 + 1

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

4 p = 1

Divide both sides

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

Divide the numbers

p = \frac{1}{4}

p = \frac{1}{4} 4 p^{2} + 4 p + 1 = 0

Solve the equation

More Steps

Evaluate

4 p^{2} + 4 p + 1 = 0

Use a^{2} + 2 ab + b^{2} = (a + b)^{2} to factor the expression

(2 p + 1)^{2} = 0

Simplify the expression

2 p + 1 = 0

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

2 p = 0 - 1

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

2 p = - 1

Divide both sides

\frac{2 p}{2} = \frac{- 1}{2}

Divide the numbers

p = \frac{- 1}{2}

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

p = - \frac{1}{2}

p = \frac{1}{4} p = - \frac{1}{2}

Solution

p_{1} = - \frac{1}{2}, p_{2} = \frac{1}{4}

Alternative Form

p_{1} = - 0.5, p_{2} = 0.25

Show Solution

(4p 1)(4p^2+4p+1)

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression