Solve (t-2)(t+5)(t-4)

Question

Simplify the expression

t^{3} - t^{2} - 22 t + 40

Evaluate

(t - 2) (t + 5) (t - 4)

Multiply the terms

More Steps

Evaluate

(t - 2) (t + 5)

Apply the distributive property

t \times t + t \times 5 - 2 t - 2 \times 5

Multiply the terms

t^{2} + t \times 5 - 2 t - 2 \times 5

Use the commutative property to reorder the terms

t^{2} + 5 t - 2 t - 2 \times 5

Multiply the numbers

t^{2} + 5 t - 2 t - 10

Subtract the terms

More Steps

Evaluate

5 t - 2 t

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

(5 - 2) t

Subtract the numbers

3 t

t^{2} + 3 t - 10

(t^{2} + 3 t - 10) (t - 4)

Apply the distributive property

t^{2} \times t - t^{2} \times 4 + 3 t \times t - 3 t \times 4 - 10 t - (- 10 \times 4)

Multiply the terms

More Steps

Evaluate

t^{2} \times t

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

t^{2 + 1}

Add the numbers

t^{3}

t^{3} - t^{2} \times 4 + 3 t \times t - 3 t \times 4 - 10 t - (- 10 \times 4)

Use the commutative property to reorder the terms

t^{3} - 4 t^{2} + 3 t \times t - 3 t \times 4 - 10 t - (- 10 \times 4)

Multiply the terms

t^{3} - 4 t^{2} + 3 t^{2} - 3 t \times 4 - 10 t - (- 10 \times 4)

Multiply the numbers

t^{3} - 4 t^{2} + 3 t^{2} - 12 t - 10 t - (- 10 \times 4)

Multiply the numbers

t^{3} - 4 t^{2} + 3 t^{2} - 12 t - 10 t - (- 40)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

t^{3} - 4 t^{2} + 3 t^{2} - 12 t - 10 t + 40

Add the terms

More Steps

Evaluate

- 4 t^{2} + 3 t^{2}

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

(- 4 + 3) t^{2}

Add the numbers

- t^{2}

t^{3} - t^{2} - 12 t - 10 t + 40

Solution

More Steps

Evaluate

- 12 t - 10 t

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

(- 12 - 10) t

Subtract the numbers

- 22 t

t^{3} - t^{2} - 22 t + 40

Show Solution

Find the roots

t_{1} = - 5, t_{2} = 2, t_{3} = 4

Evaluate

(t - 2) (t + 5) (t - 4)

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

(t - 2) (t + 5) (t - 4) = 0

Separate the equation into 3 possible cases

t - 2 = 0 t + 5 = 0 t - 4 = 0

Solve the equation

More Steps

Evaluate

t - 2 = 0

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

t = 0 + 2

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

t = 2

t = 2 t + 5 = 0 t - 4 = 0

Solve the equation

More Steps

Evaluate

t + 5 = 0

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

t = 0 - 5

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

t = - 5

t = 2 t = - 5 t - 4 = 0

Solve the equation

More Steps

Evaluate

t - 4 = 0

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

t = 0 + 4

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

t = 4

t = 2 t = - 5 t = 4

Solution

t_{1} = - 5, t_{2} = 2, t_{3} = 4

Show Solution