Solve 5q^4q-5q - ScanMath

Question

Simplify the expression

5 q^{5} - 5 q

Evaluate

5 q^{4} \times q - 5 q

Solution

More Steps

Evaluate

5 q^{4} \times q

Multiply the terms with the same base by adding their exponents

5 q^{4 + 1}

Add the numbers

5 q^{5}

5 q^{5} - 5 q

Show Solution

5 q (q - 1) (q + 1) (q^{2} + 1)

Evaluate

5 q^{4} \times q - 5 q

Evaluate

More Steps

Evaluate

5 q^{4} \times q

Multiply the terms with the same base by adding their exponents

5 q^{4 + 1}

Add the numbers

5 q^{5}

5 q^{5} - 5 q

Factor out 5 q from the expression

5 q (q^{4} - 1)

Factor the expression

More Steps

Evaluate

q^{4} - 1

Rewrite the expression in exponential form

(q^{2})^{2} - 1^{2}

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

(q^{2} - 1) (q^{2} + 1)

5 q (q^{2} - 1) (q^{2} + 1)

Solution

More Steps

Evaluate

q^{2} - 1

Rewrite the expression in exponential form

q^{2} - 1^{2}

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

(q - 1) (q + 1)

5 q (q - 1) (q + 1) (q^{2} + 1)

Show Solution

q_{1} = - 1, q_{2} = 0, q_{3} = 1

Evaluate

5 q^{4} \times q - 5 q

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

5 q^{4} \times q - 5 q = 0

Multiply

More Steps

Multiply the terms

5 q^{4} \times q

Multiply the terms with the same base by adding their exponents

5 q^{4 + 1}

Add the numbers

5 q^{5}

5 q^{5} - 5 q = 0

Factor the expression

5 q (q^{4} - 1) = 0

Divide both sides

q (q^{4} - 1) = 0

Separate the equation into 2 possible cases

q = 0 q^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

q^{4} - 1 = 0

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

q^{4} = 0 + 1

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

q^{4} = 1

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

q = \pm 41

Simplify the expression

q = \pm 1

Separate the equation into 2 possible cases

q = 1 q = - 1

q = 0 q = 1 q = - 1

Solution

q_{1} = - 1, q_{2} = 0, q_{3} = 1

Show Solution