Solve [2(a^6) - 3][3(a^6) 2]

Question

Simplify the expression

12 a^{12} - 18 a^{6}

Evaluate

(2 a^{6} - 3) (3 a^{6} \times 2)

Remove the parentheses

(2 a^{6} - 3) \times 3 a^{6} \times 2

Multiply the terms

(2 a^{6} - 3) \times 6 a^{6}

Multiply the terms

6 a^{6} (2 a^{6} - 3)

Apply the distributive property

6 a^{6} \times 2 a^{6} - 6 a^{6} \times 3

Multiply the terms

More Steps

Evaluate

6 a^{6} \times 2 a^{6}

Multiply the numbers

12 a^{6} \times a^{6}

Multiply the terms

More Steps

Evaluate

a^{6} \times a^{6}

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

a^{6 + 6}

Add the numbers

a^{12}

12 a^{12}

12 a^{12} - 6 a^{6} \times 3

Solution

12 a^{12} - 18 a^{6}

Show Solution

a_{1} = - \frac{6 96}{2}, a_{2} = 0, a_{3} = \frac{6 96}{2}

Alternative Form

a_{1} \approx - 1.069913, a_{2} = 0, a_{3} \approx 1.069913

Evaluate

(2 (a^{6}) - 3) (3 (a^{6}) \times 2)

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

(2 (a^{6}) - 3) (3 (a^{6}) \times 2) = 0

Calculate

(2 a^{6} - 3) (3 (a^{6}) \times 2) = 0

Calculate

(2 a^{6} - 3) (3 a^{6} \times 2) = 0

Multiply the terms

(2 a^{6} - 3) \times 6 a^{6} = 0

Multiply the terms

6 a^{6} (2 a^{6} - 3) = 0

Elimination the left coefficient

a^{6} (2 a^{6} - 3) = 0

Separate the equation into 2 possible cases

a^{6} = 0 2 a^{6} - 3 = 0

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

a = 0 2 a^{6} - 3 = 0

Solve the equation

More Steps

Evaluate

2 a^{6} - 3 = 0

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

2 a^{6} = 0 + 3

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

2 a^{6} = 3

Divide both sides

\frac{2 a ^{6}}{2} = \frac{3}{2}

Divide the numbers

a^{6} = \frac{3}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 6 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 3}{6 2}

Multiply by the Conjugate

\frac{6 3 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 3 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

\frac{6 96}{6 2 \times 6 2 ^{5}}

Multiply the numbers

\frac{6 96}{2}

a = \pm \frac{6 96}{2}

Separate the equation into 2 possible cases

a = \frac{6 96}{2} a = - \frac{6 96}{2}

a = 0 a = \frac{6 96}{2} a = - \frac{6 96}{2}

Solution

a_{1} = - \frac{6 96}{2}, a_{2} = 0, a_{3} = \frac{6 96}{2}

Alternative Form

a_{1} \approx - 1.069913, a_{2} = 0, a_{3} \approx 1.069913

Show Solution