Solve 6(x-4)^(3)-(x-4)^(4)

Question

Simplify the expression

22 x^{3} - 168 x^{2} + 544 x - 640 - x^{4}

Evaluate

6 (x - 4)^{3} - (x - 4)^{4}

Expand the expression

More Steps

Calculate

6 (x - 4)^{3}

Simplify

6 (x^{3} - 12 x^{2} + 48 x - 64)

Apply the distributive property

6 x^{3} - 6 \times 12 x^{2} + 6 \times 48 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 6 \times 48 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 288 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 288 x - 384

6 x^{3} - 72 x^{2} + 288 x - 384 - (x - 4)^{4}

Expand the expression

6 x^{3} - 72 x^{2} + 288 x - 384 - x^{4} + 16 x^{3} - 96 x^{2} + 256 x - 256

Add the terms

More Steps

Evaluate

6 x^{3} + 16 x^{3}

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

(6 + 16) x^{3}

Add the numbers

22 x^{3}

22 x^{3} - 72 x^{2} + 288 x - 384 - x^{4} - 96 x^{2} + 256 x - 256

Subtract the terms

More Steps

Evaluate

- 72 x^{2} - 96 x^{2}

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

(- 72 - 96) x^{2}

Subtract the numbers

- 168 x^{2}

22 x^{3} - 168 x^{2} + 288 x - 384 - x^{4} + 256 x - 256

Add the terms

More Steps

Evaluate

288 x + 256 x

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

(288 + 256) x

Add the numbers

544 x

22 x^{3} - 168 x^{2} + 544 x - 384 - x^{4} - 256

Solution

22 x^{3} - 168 x^{2} + 544 x - 640 - x^{4}

Show Solution

Factor the expression

(10 - x) (x - 4)^{3}

Evaluate

6 (x - 4)^{3} - (x - 4)^{4}

Rewrite the expression

6 (x - 4)^{3} + (- x + 4) (x - 4)^{3}

Factor out (x - 4)^{3} from the expression

(6 - x + 4) (x - 4)^{3}

Solution

(10 - x) (x - 4)^{3}

Show Solution

Find the roots

x_{1} = 4, x_{2} = 10

Evaluate

6 (x - 4)^{3} - (x - 4)^{4}

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

6 (x - 4)^{3} - (x - 4)^{4} = 0

Calculate

More Steps

Evaluate

6 (x - 4)^{3} - (x - 4)^{4}

Expand the expression

More Steps

Calculate

6 (x - 4)^{3}

Simplify

6 (x^{3} - 12 x^{2} + 48 x - 64)

Apply the distributive property

6 x^{3} - 6 \times 12 x^{2} + 6 \times 48 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 6 \times 48 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 288 x - 6 \times 64

Multiply the numbers

6 x^{3} - 72 x^{2} + 288 x - 384

6 x^{3} - 72 x^{2} + 288 x - 384 - (x - 4)^{4}

Expand the expression

6 x^{3} - 72 x^{2} + 288 x - 384 - x^{4} + 16 x^{3} - 96 x^{2} + 256 x - 256

Add the terms

More Steps

Evaluate

6 x^{3} + 16 x^{3}

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

(6 + 16) x^{3}

Add the numbers

22 x^{3}

22 x^{3} - 72 x^{2} + 288 x - 384 - x^{4} - 96 x^{2} + 256 x - 256

Subtract the terms

More Steps

Evaluate

- 72 x^{2} - 96 x^{2}

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

(- 72 - 96) x^{2}

Subtract the numbers

- 168 x^{2}

22 x^{3} - 168 x^{2} + 288 x - 384 - x^{4} + 256 x - 256

Add the terms

More Steps

Evaluate

288 x + 256 x

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

(288 + 256) x

Add the numbers

544 x

22 x^{3} - 168 x^{2} + 544 x - 384 - x^{4} - 256

Subtract the numbers

22 x^{3} - 168 x^{2} + 544 x - 640 - x^{4}

22 x^{3} - 168 x^{2} + 544 x - 640 - x^{4} = 0

Factor the expression

(- 10 + x) (4 - x)^{3} = 0

Separate the equation into 2 possible cases

- 10 + x = 0 (4 - x)^{3} = 0

Solve the equation

More Steps

Evaluate

- 10 + x = 0

Move the constant to the right side

x = 0 + 10

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

x = 10

x = 10 (4 - x)^{3} = 0

Solve the equation

More Steps

Evaluate

(4 - x)^{3} = 0

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

4 - x = 0

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

- x = 0 - 4

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

- x = - 4

Change the signs on both sides of the equation

x = 4

x = 10 x = 4

Solution

x_{1} = 4, x_{2} = 10

Show Solution