Solve (2-3x)^2 (x-3)(2-3x)

Question

Simplify the expression

116 x - 24 - 198 x^{2} + 135 x^{3} - 27 x^{4}

Evaluate

(2 - 3 x)^{2} (x - 3) (2 - 3 x)

Multiply the terms with the same base by adding their exponents

(2 - 3 x)^{2 + 1} (x - 3)

Add the numbers

(2 - 3 x)^{3} (x - 3)

Expand the expression

More Steps

(8 - 36 x + 54 x^{2} - 27 x^{3}) (x - 3)

Apply the distributive property

8 x - 8 \times 3 - 36 x \times x - (- 36 x \times 3) + 54 x^{2} \times x - 54 x^{2} \times 3 - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the numbers

8 x - 24 - 36 x \times x - (- 36 x \times 3) + 54 x^{2} \times x - 54 x^{2} \times 3 - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the terms

8 x - 24 - 36 x^{2} - (- 36 x \times 3) + 54 x^{2} \times x - 54 x^{2} \times 3 - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the numbers

8 x - 24 - 36 x^{2} - (- 108 x) + 54 x^{2} \times x - 54 x^{2} \times 3 - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the terms

More Steps

8 x - 24 - 36 x^{2} - (- 108 x) + 54 x^{3} - 54 x^{2} \times 3 - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the numbers

8 x - 24 - 36 x^{2} - (- 108 x) + 54 x^{3} - 162 x^{2} - 27 x^{3} \times x - (- 27 x^{3} \times 3)

Multiply the terms

More Steps

8 x - 24 - 36 x^{2} - (- 108 x) + 54 x^{3} - 162 x^{2} - 27 x^{4} - (- 27 x^{3} \times 3)

Multiply the numbers

8 x - 24 - 36 x^{2} - (- 108 x) + 54 x^{3} - 162 x^{2} - 27 x^{4} - (- 81 x^{3})

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

8 x - 24 - 36 x^{2} + 108 x + 54 x^{3} - 162 x^{2} - 27 x^{4} + 81 x^{3}

Add the terms

More Steps

116 x - 24 - 36 x^{2} + 54 x^{3} - 162 x^{2} - 27 x^{4} + 81 x^{3}

Subtract the terms

More Steps

116 x - 24 - 198 x^{2} + 54 x^{3} - 27 x^{4} + 81 x^{3}

Solution

More Steps

116 x - 24 - 198 x^{2} + 135 x^{3} - 27 x^{4}

Show Solution

Find the roots

x_{1} = \frac{2}{3}, x_{2} = 3

Alternative Form

x_{1} = 0. \dot{6}, x_{2} = 3

Show Solution