Solve (q^2-4)(q-5)

Question

Simplify the expression

q^{3} - 5 q^{2} - 4 q + 20

Evaluate

(q^{2} - 4) (q - 5)

Apply the distributive property

q^{2} \times q - q^{2} \times 5 - 4 q - (- 4 \times 5)

Multiply the terms

More Steps

Evaluate

q^{2} \times q

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

q^{2 + 1}

Add the numbers

q^{3}

q^{3} - q^{2} \times 5 - 4 q - (- 4 \times 5)

Use the commutative property to reorder the terms

q^{3} - 5 q^{2} - 4 q - (- 4 \times 5)

Multiply the numbers

q^{3} - 5 q^{2} - 4 q - (- 20)

Solution

q^{3} - 5 q^{2} - 4 q + 20

Show Solution

(q - 2) (q + 2) (q - 5)

Evaluate

(q^{2} - 4) (q - 5)

Solution

(q - 2) (q + 2) (q - 5)

Show Solution

q_{1} = - 2, q_{2} = 2, q_{3} = 5

Evaluate

(q^{2} - 4) (q - 5)

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

(q^{2} - 4) (q - 5) = 0

Separate the equation into 2 possible cases

q^{2} - 4 = 0 q - 5 = 0

Solve the equation

More Steps

Evaluate

q^{2} - 4 = 0

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

q^{2} = 0 + 4

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

q^{2} = 4

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

q = \pm 4

Simplify the expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

q = \pm 2

Separate the equation into 2 possible cases

q = 2 q = - 2

q = 2 q = - 2 q - 5 = 0

Solve the equation

More Steps

Evaluate

q - 5 = 0

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

q = 0 + 5

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

q = 5

q = 2 q = - 2 q = 5

Solution

q_{1} = - 2, q_{2} = 2, q_{3} = 5

Show Solution