Solve (6-c)(2c^2) (22-4c)(c^2)

Question

Simplify the expression

264 c^{4} - 92 c^{5} + 8 c^{6}

Evaluate

(6 - c) \times 2 c^{2} (22 - 4 c) c^{2}

Multiply the terms with the same base by adding their exponents

(6 - c) \times 2 c^{2 + 2} (22 - 4 c)

Add the numbers

(6 - c) \times 2 c^{4} (22 - 4 c)

Multiply the first two terms

2 c^{4} (6 - c) (22 - 4 c)

Multiply the terms

More Steps

Evaluate

2 c^{4} (6 - c)

Apply the distributive property

2 c^{4} \times 6 - 2 c^{4} \times c

Multiply the numbers

12 c^{4} - 2 c^{4} \times c

Multiply the terms

More Steps

Evaluate

c^{4} \times c

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

c^{4 + 1}

Add the numbers

c^{5}

12 c^{4} - 2 c^{5}

(12 c^{4} - 2 c^{5}) (22 - 4 c)

Apply the distributive property

12 c^{4} \times 22 - 12 c^{4} \times 4 c - 2 c^{5} \times 22 - (- 2 c^{5} \times 4 c)

Multiply the numbers

264 c^{4} - 12 c^{4} \times 4 c - 2 c^{5} \times 22 - (- 2 c^{5} \times 4 c)

Multiply the terms

More Steps

Evaluate

12 c^{4} \times 4 c

Multiply the numbers

48 c^{4} \times c

Multiply the terms

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Evaluate

c^{4} \times c

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

c^{4 + 1}

Add the numbers

c^{5}

48 c^{5}

264 c^{4} - 48 c^{5} - 2 c^{5} \times 22 - (- 2 c^{5} \times 4 c)

Multiply the numbers

264 c^{4} - 48 c^{5} - 44 c^{5} - (- 2 c^{5} \times 4 c)

Multiply the terms

More Steps

Evaluate

- 2 c^{5} \times 4 c

Multiply the numbers

- 8 c^{5} \times c

Multiply the terms

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Evaluate

c^{5} \times c

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

c^{5 + 1}

Add the numbers

c^{6}

- 8 c^{6}

264 c^{4} - 48 c^{5} - 44 c^{5} - (- 8 c^{6})

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

264 c^{4} - 48 c^{5} - 44 c^{5} + 8 c^{6}

Solution

More Steps

Evaluate

- 48 c^{5} - 44 c^{5}

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

(- 48 - 44) c^{5}

Subtract the numbers

- 92 c^{5}

264 c^{4} - 92 c^{5} + 8 c^{6}

Show Solution

Factor the expression

4 c^{4} (6 - c) (11 - 2 c)

Evaluate

(6 - c) \times 2 c^{2} (22 - 4 c) c^{2}

Multiply the terms with the same base by adding their exponents

(6 - c) \times 2 c^{2 + 2} (22 - 4 c)

Add the numbers

(6 - c) \times 2 c^{4} (22 - 4 c)

Multiply the first two terms

2 c^{4} (6 - c) (22 - 4 c)

Factor the expression

2 c^{4} (6 - c) \times 2 (11 - 2 c)

Solution

4 c^{4} (6 - c) (11 - 2 c)

Show Solution

Find the roots

c_{1} = 0, c_{2} = \frac{11}{2}, c_{3} = 6

Alternative Form

c_{1} = 0, c_{2} = 5.5, c_{3} = 6

Evaluate

(6 - c) (2 c^{2}) (22 - 4 c) (c^{2})

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

(6 - c) (2 c^{2}) (22 - 4 c) (c^{2}) = 0

Multiply the terms

(6 - c) \times 2 c^{2} (22 - 4 c) (c^{2}) = 0

Calculate

(6 - c) \times 2 c^{2} (22 - 4 c) c^{2} = 0

Multiply the terms

More Steps

Multiply the terms

(6 - c) \times 2 c^{2} (22 - 4 c) c^{2}

Multiply the terms with the same base by adding their exponents

(6 - c) \times 2 c^{2 + 2} (22 - 4 c)

Add the numbers

(6 - c) \times 2 c^{4} (22 - 4 c)

Multiply the first two terms

2 c^{4} (6 - c) (22 - 4 c)

2 c^{4} (6 - c) (22 - 4 c) = 0

Elimination the left coefficient

c^{4} (6 - c) (22 - 4 c) = 0

Separate the equation into 3 possible cases

c^{4} = 0 6 - c = 0 22 - 4 c = 0

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

c = 0 6 - c = 0 22 - 4 c = 0

Solve the equation

More Steps

Evaluate

6 - c = 0

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

- c = 0 - 6

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

- c = - 6

Change the signs on both sides of the equation

c = 6

c = 0 c = 6 22 - 4 c = 0

Solve the equation

More Steps

Evaluate

22 - 4 c = 0

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

- 4 c = 0 - 22

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

- 4 c = - 22

Change the signs on both sides of the equation

4 c = 22

Divide both sides

\frac{4 c}{4} = \frac{22}{4}

Divide the numbers

c = \frac{22}{4}

Cancel out the common factor 2

c = \frac{11}{2}

c = 0 c = 6 c = \frac{11}{2}

Solution

c_{1} = 0, c_{2} = \frac{11}{2}, c_{3} = 6

Alternative Form

c_{1} = 0, c_{2} = 5.5, c_{3} = 6

Show Solution