Solve (p-1)(p^22p^3)

Question

Simplify the expression

2 p^{6} - 2 p^{5}

Evaluate

(p - 1) (p^{2} \times 2 p^{3})

Remove the parentheses

(p - 1) p^{2} \times 2 p^{3}

Multiply the terms with the same base by adding their exponents

(p - 1) p^{2 + 3} \times 2

Add the numbers

(p - 1) p^{5} \times 2

Use the commutative property to reorder the terms

(p - 1) \times 2 p^{5}

Multiply the terms

2 p^{5} (p - 1)

Apply the distributive property

2 p^{5} \times p - 2 p^{5} \times 1

Multiply the terms

More Steps

Evaluate

p^{5} \times p

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

p^{5 + 1}

Add the numbers

p^{6}

2 p^{6} - 2 p^{5} \times 1

Solution

2 p^{6} - 2 p^{5}

Show Solution

p_{1} = 0, p_{2} = 1

Evaluate

(p - 1) (p^{2} \times 2 p^{3})

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

(p - 1) (p^{2} \times 2 p^{3}) = 0

Multiply

More Steps

Multiply the terms

p^{2} \times 2 p^{3}

Multiply the terms with the same base by adding their exponents

p^{2 + 3} \times 2

Add the numbers

p^{5} \times 2

Use the commutative property to reorder the terms

2 p^{5}

(p - 1) \times 2 p^{5} = 0

Multiply the terms

2 p^{5} (p - 1) = 0

Elimination the left coefficient

p^{5} (p - 1) = 0

Separate the equation into 2 possible cases

p^{5} = 0 p - 1 = 0

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

p = 0 p - 1 = 0

Solve the equation

More Steps

Evaluate

p - 1 = 0

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

p = 0 + 1

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

p = 1

p = 0 p = 1

Solution

p_{1} = 0, p_{2} = 1

Show Solution