Solve (c^2 8c 16)(16-8c c^2)

Question

Simplify the expression

2048 c^{3} - 1024 c^{6}

Evaluate

(c^{2} \times 8 c \times 16) (16 - 8 c \times c^{2})

Remove the parentheses

c^{2} \times 8 c \times 16 (16 - 8 c \times c^{2})

Multiply

More Steps

Multiply the terms

8 c \times c^{2}

Multiply the terms with the same base by adding their exponents

8 c^{1 + 2}

Add the numbers

8 c^{3}

c^{2} \times 8 c \times 16 (16 - 8 c^{3})

Multiply the terms with the same base by adding their exponents

c^{2 + 1} \times 8 \times 16 (16 - 8 c^{3})

Add the numbers

c^{3} \times 8 \times 16 (16 - 8 c^{3})

Multiply the terms

c^{3} \times 128 (16 - 8 c^{3})

Use the commutative property to reorder the terms

128 c^{3} (16 - 8 c^{3})

Apply the distributive property

128 c^{3} \times 16 - 128 c^{3} \times 8 c^{3}

Multiply the numbers

2048 c^{3} - 128 c^{3} \times 8 c^{3}

Solution

More Steps

Evaluate

128 c^{3} \times 8 c^{3}

Multiply the numbers

1024 c^{3} \times c^{3}

Multiply the terms

More Steps

Evaluate

c^{3} \times c^{3}

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

c^{3 + 3}

Add the numbers

c^{6}

1024 c^{6}

2048 c^{3} - 1024 c^{6}

Show Solution

Factor the expression

1024 c^{3} (2 - c^{3})

Evaluate

(c^{2} \times 8 c \times 16) (16 - 8 c \times c^{2})

Remove the parentheses

c^{2} \times 8 c \times 16 (16 - 8 c \times c^{2})

Multiply

More Steps

Multiply the terms

8 c \times c^{2}

Multiply the terms with the same base by adding their exponents

8 c^{1 + 2}

Add the numbers

8 c^{3}

c^{2} \times 8 c \times 16 (16 - 8 c^{3})

Multiply

More Steps

Multiply the terms

c^{2} \times 8 c \times 16

Multiply the terms with the same base by adding their exponents

c^{2 + 1} \times 8 \times 16

Add the numbers

c^{3} \times 8 \times 16

Multiply the terms

c^{3} \times 128

Use the commutative property to reorder the terms

128 c^{3}

128 c^{3} (16 - 8 c^{3})

Factor the expression

128 c^{3} \times 8 (2 - c^{3})

Solution

1024 c^{3} (2 - c^{3})

Show Solution

Find the roots

c_{1} = 0, c_{2} = 32

Alternative Form

c_{1} = 0, c_{2} \approx 1.259921

Evaluate

(c^{2} \times 8 c \times 16) (16 - 8 c \times c^{2})

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

(c^{2} \times 8 c \times 16) (16 - 8 c \times c^{2}) = 0

Multiply

More Steps

Multiply the terms

c^{2} \times 8 c \times 16

Multiply the terms with the same base by adding their exponents

c^{2 + 1} \times 8 \times 16

Add the numbers

c^{3} \times 8 \times 16

Multiply the terms

c^{3} \times 128

Use the commutative property to reorder the terms

128 c^{3}

128 c^{3} (16 - 8 c \times c^{2}) = 0

Multiply

More Steps

Multiply the terms

8 c \times c^{2}

Multiply the terms with the same base by adding their exponents

8 c^{1 + 2}

Add the numbers

8 c^{3}

128 c^{3} (16 - 8 c^{3}) = 0

Elimination the left coefficient

c^{3} (16 - 8 c^{3}) = 0

Separate the equation into 2 possible cases

c^{3} = 0 16 - 8 c^{3} = 0

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

c = 0 16 - 8 c^{3} = 0

Solve the equation

More Steps

Evaluate

16 - 8 c^{3} = 0

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

- 8 c^{3} = 0 - 16

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

- 8 c^{3} = - 16

Change the signs on both sides of the equation

8 c^{3} = 16

Divide both sides

\frac{8 c ^{3}}{8} = \frac{16}{8}

Divide the numbers

c^{3} = \frac{16}{8}

Divide the numbers

More Steps

Evaluate

\frac{16}{8}

Reduce the numbers

\frac{2}{1}

Calculate

2

c^{3} = 2

Take the 3 -th root on both sides of the equation

3 c^{3} = 32

Calculate

c = 32

c = 0 c = 32

Solution

c_{1} = 0, c_{2} = 32

Alternative Form

c_{1} = 0, c_{2} \approx 1.259921

Show Solution