Solve a^4 3a^3 2a^2-a

Question

Simplify the expression

6 a^{9} - a

Evaluate

a^{4} \times 3 a^{3} \times 2 a^{2} - a

Solution

More Steps

Evaluate

a^{4} \times 3 a^{3} \times 2 a^{2}

Multiply the terms with the same base by adding their exponents

a^{4 + 3 + 2} \times 3 \times 2

Add the numbers

a^{9} \times 3 \times 2

Multiply the terms

a^{9} \times 6

Use the commutative property to reorder the terms

6 a^{9}

6 a^{9} - a

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Factor the expression

a (6 a^{8} - 1)

Evaluate

a^{4} \times 3 a^{3} \times 2 a^{2} - a

Multiply

More Steps

Evaluate

a^{4} \times 3 a^{3} \times 2 a^{2}

Multiply the terms with the same base by adding their exponents

a^{4 + 3 + 2} \times 3 \times 2

Add the numbers

a^{9} \times 3 \times 2

Multiply the terms

a^{9} \times 6

Use the commutative property to reorder the terms

6 a^{9}

6 a^{9} - a

Rewrite the expression

a \times 6 a^{8} - a

Solution

a (6 a^{8} - 1)

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Find the roots

a_{1} = - \frac{8 6 ^{7}}{6}, a_{2} = 0, a_{3} = \frac{8 6 ^{7}}{6}

Alternative Form

a_{1} \approx - 0.799339, a_{2} = 0, a_{3} \approx 0.799339

Evaluate

a^{4} \times 3 a^{3} \times 2 a^{2} - a

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

a^{4} \times 3 a^{3} \times 2 a^{2} - a = 0

Multiply

More Steps

Multiply the terms

a^{4} \times 3 a^{3} \times 2 a^{2}

Multiply the terms with the same base by adding their exponents

a^{4 + 3 + 2} \times 3 \times 2

Add the numbers

a^{9} \times 3 \times 2

Multiply the terms

a^{9} \times 6

Use the commutative property to reorder the terms

6 a^{9}

6 a^{9} - a = 0

Factor the expression

a (6 a^{8} - 1) = 0

Separate the equation into 2 possible cases

a = 0 6 a^{8} - 1 = 0

Solve the equation

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Evaluate

6 a^{8} - 1 = 0

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

6 a^{8} = 0 + 1

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

6 a^{8} = 1

Divide both sides

\frac{6 a ^{8}}{6} = \frac{1}{6}

Divide the numbers

a^{8} = \frac{1}{6}

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

a = \pm 8 \frac{1}{6}

Simplify the expression

More Steps

Evaluate

8 \frac{1}{6}

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

\frac{8 1}{8 6}

Simplify the radical expression

\frac{1}{8 6}

Multiply by the Conjugate

\frac{8 6 ^{7}}{8 6 \times 8 6 ^{7}}

Multiply the numbers

\frac{8 6 ^{7}}{6}

a = \pm \frac{8 6 ^{7}}{6}

Separate the equation into 2 possible cases

a = \frac{8 6 ^{7}}{6} a = - \frac{8 6 ^{7}}{6}

a = 0 a = \frac{8 6 ^{7}}{6} a = - \frac{8 6 ^{7}}{6}

Solution

a_{1} = - \frac{8 6 ^{7}}{6}, a_{2} = 0, a_{3} = \frac{8 6 ^{7}}{6}

Alternative Form

a_{1} \approx - 0.799339, a_{2} = 0, a_{3} \approx 0.799339

Show Solution