Solve ((x-1)/12x^3 24x^2) ((3x^2)/12x^3 24x^2)

Question

Simplify the expression

12 x^{13} - 12 x^{12}

Evaluate

(\frac{x - 1}{12} \times x^{3} \times 24 x^{2}) (\frac{3 x ^{2}}{12} x^{3} \times 24 x^{2})

Remove the parentheses

\frac{x - 1}{12} \times x^{3} \times 24 x^{2} \times \frac{3 x ^{2}}{12} x^{3} \times 24 x^{2}

Cancel out the common factor 3

\frac{x - 1}{12} \times x^{3} \times 24 x^{2} \times \frac{x ^{2}}{4} x^{3} \times 24 x^{2}

Multiply the terms with the same base by adding their exponents

\frac{x - 1}{12} \times x^{3 + 2 + 3 + 2} \times 24 \times \frac{x ^{2}}{4} \times 24

Add the numbers

\frac{x - 1}{12} \times x^{10} \times 24 \times \frac{x ^{2}}{4} \times 24

Multiply the terms

\frac{x - 1}{12} \times x^{10} \times 576 \times \frac{x ^{2}}{4}

Multiply the terms

More Steps

Multiply the terms

\frac{x - 1}{12} \times x^{10}

Multiply the terms

\frac{( x - 1 ) x ^{10}}{12}

Multiply the terms

\frac{x ^{10} ( x - 1 )}{12}

\frac{x ^{10} ( x - 1 )}{12} \times 576 \times \frac{x ^{2}}{4}

Multiply the terms

More Steps

Multiply the terms

\frac{x ^{10} ( x - 1 )}{12} \times 576

Cancel out the common factor 12

x^{10} (x - 1) \times 48

Use the commutative property to reorder the terms

48 x^{10} (x - 1)

48 x^{10} (x - 1) \times \frac{x ^{2}}{4}

Cancel out the common factor 4

12 x^{10} (x - 1) x^{2}

Multiply the terms

More Steps

Evaluate

x^{10} \times x^{2}

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

x^{10 + 2}

Add the numbers

x^{12}

12 x^{12} (x - 1)

Apply the distributive property

12 x^{12} \times x - 12 x^{12} \times 1

Multiply the terms

More Steps

Evaluate

x^{12} \times x

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

x^{12 + 1}

Add the numbers

x^{13}

12 x^{13} - 12 x^{12} \times 1

Solution

12 x^{13} - 12 x^{12}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1

Evaluate

(\frac{x - 1}{12} \times x^{3} \times 24 x^{2}) (\frac{3 x ^{2}}{12} x^{3} \times 24 x^{2})

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

(\frac{x - 1}{12} \times x^{3} \times 24 x^{2}) (\frac{3 x ^{2}}{12} x^{3} \times 24 x^{2}) = 0

Multiply

More Steps

Multiply the terms

\frac{x - 1}{12} \times x^{3} \times 24 x^{2}

Multiply the terms with the same base by adding their exponents

\frac{x - 1}{12} \times x^{3 + 2} \times 24

Add the numbers

\frac{x - 1}{12} \times x^{5} \times 24

Multiply the terms

More Steps

Multiply the terms

\frac{x - 1}{12} \times x^{5}

Multiply the terms

\frac{( x - 1 ) x ^{5}}{12}

Multiply the terms

\frac{x ^{5} ( x - 1 )}{12}

\frac{x ^{5} ( x - 1 )}{12} \times 24

Cancel out the common factor 12

x^{5} (x - 1) \times 2

Use the commutative property to reorder the terms

2 x^{5} (x - 1)

2 x^{5} (x - 1) (\frac{3 x ^{2}}{12} x^{3} \times 24 x^{2}) = 0

Cancel out the common factor 3

2 x^{5} (x - 1) (\frac{x ^{2}}{4} x^{3} \times 24 x^{2}) = 0

Multiply

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{3} \times 24 x^{2}

Multiply the terms with the same base by adding their exponents

\frac{x ^{2}}{4} x^{3 + 2} \times 24

Add the numbers

\frac{x ^{2}}{4} x^{5} \times 24

Multiply the terms

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{5}

Multiply the terms

\frac{x ^{2} \times x ^{5}}{4}

Multiply the terms

\frac{x ^{7}}{4}

\frac{x ^{7}}{4} \times 24

Cancel out the common factor 4

x^{7} \times 6

Use the commutative property to reorder the terms

6 x^{7}

2 x^{5} (x - 1) \times 6 x^{7} = 0

Multiply

More Steps

Evaluate

2 x^{5} (x - 1) \times 6 x^{7}

Multiply the terms

12 x^{5} (x - 1) x^{7}

Multiply the terms

More Steps

Evaluate

x^{5} \times x^{7}

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

x^{5 + 7}

Add the numbers

x^{12}

12 x^{12} (x - 1)

12 x^{12} (x - 1) = 0

Elimination the left coefficient

x^{12} (x - 1) = 0

Separate the equation into 2 possible cases

x^{12} = 0 x - 1 = 0

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

x = 0 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1

Solution

x_{1} = 0, x_{2} = 1

Show Solution