Solve (4x - 2) (8x - 9) (8x - 9)

Question

Simplify the expression

256 x^{3} - 704 x^{2} + 612 x - 162

Evaluate

(4 x - 2) (8 x - 9) (8 x - 9)

Multiply the terms

(4 x - 2) (8 x - 9)^{2}

Expand the expression

More Steps

Evaluate

(8 x - 9)^{2}

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

(8 x)^{2} - 2 \times 8 x \times 9 + 9^{2}

Calculate

64 x^{2} - 144 x + 81

(4 x - 2) (64 x^{2} - 144 x + 81)

Apply the distributive property

4 x \times 64 x^{2} - 4 x \times 144 x + 4 x \times 81 - 2 \times 64 x^{2} - (- 2 \times 144 x) - 2 \times 81

Multiply the terms

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Evaluate

4 x \times 64 x^{2}

Multiply the numbers

256 x \times x^{2}

Multiply the terms

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Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

256 x^{3}

256 x^{3} - 4 x \times 144 x + 4 x \times 81 - 2 \times 64 x^{2} - (- 2 \times 144 x) - 2 \times 81

Multiply the terms

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Evaluate

4 x \times 144 x

Multiply the numbers

576 x \times x

Multiply the terms

576 x^{2}

256 x^{3} - 576 x^{2} + 4 x \times 81 - 2 \times 64 x^{2} - (- 2 \times 144 x) - 2 \times 81

Multiply the numbers

256 x^{3} - 576 x^{2} + 324 x - 2 \times 64 x^{2} - (- 2 \times 144 x) - 2 \times 81

Multiply the numbers

256 x^{3} - 576 x^{2} + 324 x - 128 x^{2} - (- 2 \times 144 x) - 2 \times 81

Multiply the numbers

256 x^{3} - 576 x^{2} + 324 x - 128 x^{2} - (- 288 x) - 2 \times 81

Multiply the numbers

256 x^{3} - 576 x^{2} + 324 x - 128 x^{2} - (- 288 x) - 162

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

256 x^{3} - 576 x^{2} + 324 x - 128 x^{2} + 288 x - 162

Subtract the terms

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Evaluate

- 576 x^{2} - 128 x^{2}

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

(- 576 - 128) x^{2}

Subtract the numbers

- 704 x^{2}

256 x^{3} - 704 x^{2} + 324 x + 288 x - 162

Solution

More Steps

Evaluate

324 x + 288 x

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

(324 + 288) x

Add the numbers

612 x

256 x^{3} - 704 x^{2} + 612 x - 162

Show Solution

Factor the expression

2 (8 x - 9)^{2} (2 x - 1)

Evaluate

(4 x - 2) (8 x - 9) (8 x - 9)

Multiply the terms

(8 x - 9)^{2} (4 x - 2)

Factor the expression

(8 x - 9)^{2} \times 2 (2 x - 1)

Solution

2 (8 x - 9)^{2} (2 x - 1)

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = \frac{9}{8}

Alternative Form

x_{1} = 0.5, x_{2} = 1.125

Evaluate

(4 x - 2) (8 x - 9) (8 x - 9)

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

(4 x - 2) (8 x - 9) (8 x - 9) = 0

Multiply the terms

(4 x - 2) (8 x - 9)^{2} = 0

Separate the equation into 2 possible cases

4 x - 2 = 0 (8 x - 9)^{2} = 0

Solve the equation

More Steps

Evaluate

4 x - 2 = 0

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

4 x = 0 + 2

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

4 x = 2

Divide both sides

\frac{4 x}{4} = \frac{2}{4}

Divide the numbers

x = \frac{2}{4}

Cancel out the common factor 2

x = \frac{1}{2}

x = \frac{1}{2} (8 x - 9)^{2} = 0

Solve the equation

More Steps

Evaluate

(8 x - 9)^{2} = 0

The only way a power can be 0 is when the base equals 0

8 x - 9 = 0

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

8 x = 0 + 9

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

8 x = 9

Divide both sides

\frac{8 x}{8} = \frac{9}{8}

Divide the numbers

x = \frac{9}{8}

x = \frac{1}{2} x = \frac{9}{8}

Solution

x_{1} = \frac{1}{2}, x_{2} = \frac{9}{8}

Alternative Form

x_{1} = 0.5, x_{2} = 1.125

Show Solution