Solve (3t-4)^(2)-9t⋅(t-2)

Question

Simplify the expression

- 6 t + 16

Evaluate

(3 t - 4)^{2} - 9 t (t - 2)

Expand the expression

9 t^{2} - 24 t + 16 - 9 t (t - 2)

Expand the expression

More Steps

Calculate

- 9 t (t - 2)

Apply the distributive property

- 9 t \times t - (- 9 t \times 2)

Multiply the terms

- 9 t^{2} - (- 9 t \times 2)

Multiply the numbers

- 9 t^{2} - (- 18 t)

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

- 9 t^{2} + 18 t

9 t^{2} - 24 t + 16 - 9 t^{2} + 18 t

The sum of two opposites equals 0

More Steps

Evaluate

9 t^{2} - 9 t^{2}

Collect like terms

(9 - 9) t^{2}

Add the coefficients

0 \times t^{2}

Calculate

0

0 - 24 t + 16 + 18 t

Remove 0

- 24 t + 16 + 18 t

Solution

More Steps

Evaluate

- 24 t + 18 t

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

(- 24 + 18) t

Add the numbers

- 6 t

- 6 t + 16

Show Solution

Factor the expression

- 2 (3 t - 8)

Evaluate

(3 t - 4)^{2} - 9 t (t - 2)

Simplify

More Steps

Evaluate

(3 t - 4)^{2}

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

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

Calculate

9 t^{2} - 24 t + 16

9 t^{2} - 24 t + 16 - 9 t (t - 2)

Simplify

More Steps

Evaluate

- 9 t (t - 2)

Apply the distributive property

- 9 t \times t - 9 t (- 2)

Multiply the terms

- 9 t^{2} - 9 t (- 2)

Multiply the terms

More Steps

Evaluate

- 9 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

9 \times 2

Multiply the numbers

18

- 9 t^{2} + 18 t

9 t^{2} - 24 t + 16 - 9 t^{2} + 18 t

The sum of two opposites equals 0

More Steps

Evaluate

9 t^{2} - 9 t^{2}

Collect like terms

(9 - 9) t^{2}

Add the coefficients

0 \times t^{2}

Calculate

0

0 - 24 t + 16 + 18 t

Remove 0

- 24 t + 16 + 18 t

Add the terms

More Steps

Evaluate

- 24 t + 18 t

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

(- 24 + 18) t

Add the numbers

- 6 t

- 6 t + 16

Solution

- 2 (3 t - 8)

Show Solution

Find the roots

t = \frac{8}{3}

Alternative Form

t = 2. \dot{6}

Evaluate

(3 t - 4)^{2} - 9 t (t - 2)

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

(3 t - 4)^{2} - 9 t (t - 2) = 0

Calculate

More Steps

Evaluate

(3 t - 4)^{2} - 9 t (t - 2)

Expand the expression

9 t^{2} - 24 t + 16 - 9 t (t - 2)

Expand the expression

More Steps

Calculate

- 9 t (t - 2)

Apply the distributive property

- 9 t \times t - (- 9 t \times 2)

Multiply the terms

- 9 t^{2} - (- 9 t \times 2)

Multiply the numbers

- 9 t^{2} - (- 18 t)

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

- 9 t^{2} + 18 t

9 t^{2} - 24 t + 16 - 9 t^{2} + 18 t

The sum of two opposites equals 0

More Steps

Evaluate

9 t^{2} - 9 t^{2}

Collect like terms

(9 - 9) t^{2}

Add the coefficients

0 \times t^{2}

Calculate

0

0 - 24 t + 16 + 18 t

Remove 0

- 24 t + 16 + 18 t

Add the terms

More Steps

Evaluate

- 24 t + 18 t

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

(- 24 + 18) t

Add the numbers

- 6 t

- 6 t + 16

- 6 t + 16 = 0

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

- 6 t = 0 - 16

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

- 6 t = - 16

Change the signs on both sides of the equation

6 t = 16

Divide both sides

\frac{6 t}{6} = \frac{16}{6}

Divide the numbers

t = \frac{16}{6}

Solution

t = \frac{8}{3}

Alternative Form

t = 2. \dot{6}

Show Solution