Solve p^2 8p - 64

Question

Simplify the expression

8 p^{3} - 64

Evaluate

p^{2} \times 8 p - 64

Solution

More Steps

Evaluate

p^{2} \times 8 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 8

Add the numbers

p^{3} \times 8

Use the commutative property to reorder the terms

8 p^{3}

8 p^{3} - 64

Show Solution

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

Evaluate

p^{2} \times 8 p - 64

Evaluate

More Steps

Evaluate

p^{2} \times 8 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 8

Add the numbers

p^{3} \times 8

Use the commutative property to reorder the terms

8 p^{3}

8 p^{3} - 64

Factor out 8 from the expression

8 (p^{3} - 8)

Solution

More Steps

Evaluate

p^{3} - 8

Rewrite the expression in exponential form

p^{3} - 2^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(p - 2) (p^{2} + p \times 2 + 2^{2})

Use the commutative property to reorder the terms

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

Evaluate

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

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

Show Solution

p = 2

Evaluate

p^{2} \times 8 p - 64

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

p^{2} \times 8 p - 64 = 0

Multiply

More Steps

Multiply the terms

p^{2} \times 8 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 8

Add the numbers

p^{3} \times 8

Use the commutative property to reorder the terms

8 p^{3}

8 p^{3} - 64 = 0

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

8 p^{3} = 0 + 64

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

8 p^{3} = 64

Divide both sides

\frac{8 p ^{3}}{8} = \frac{64}{8}

Divide the numbers

p^{3} = \frac{64}{8}

Divide the numbers

More Steps

Evaluate

\frac{64}{8}

Reduce the numbers

\frac{8}{1}

Calculate

8

p^{3} = 8

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

3 p^{3} = 38

Calculate

p = 38

Solution

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

p = 2

Show Solution