Solve 3j^22j^26j^2-4j^2 j^2

Question

Simplify the expression

36 j^{6} - 4 j^{4}

Evaluate

3 j^{2} \times 2 j^{2} \times 6 j^{2} - 4 j^{2} \times j^{2}

Multiply

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Multiply the terms

3 j^{2} \times 2 j^{2} \times 6 j^{2}

Multiply the terms

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Evaluate

3 \times 2 \times 6

Multiply the terms

6 \times 6

Multiply the numbers

36

36 j^{2} \times j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

36 j^{2 + 2 + 2}

Add the numbers

36 j^{6}

36 j^{6} - 4 j^{2} \times j^{2}

Solution

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Multiply the terms

4 j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

4 j^{2 + 2}

Add the numbers

4 j^{4}

36 j^{6} - 4 j^{4}

Show Solution

Factor the expression

4 j^{4} (3 j - 1) (3 j + 1)

Evaluate

3 j^{2} \times 2 j^{2} \times 6 j^{2} - 4 j^{2} \times j^{2}

Evaluate

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Evaluate

3 j^{2} \times 2 j^{2} \times 6 j^{2}

Multiply the terms

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Evaluate

3 \times 2 \times 6

Multiply the terms

6 \times 6

Multiply the numbers

36

36 j^{2} \times j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

36 j^{2 + 2 + 2}

Add the numbers

36 j^{6}

36 j^{6} - 4 j^{2} \times j^{2}

Evaluate

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Evaluate

4 j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

4 j^{2 + 2}

Add the numbers

4 j^{4}

36 j^{6} - 4 j^{4}

Factor out 4 j^{4} from the expression

4 j^{4} (9 j^{2} - 1)

Solution

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Evaluate

9 j^{2} - 1

Rewrite the expression in exponential form

(3 j)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(3 j - 1) (3 j + 1)

4 j^{4} (3 j - 1) (3 j + 1)

Show Solution

Find the roots

j_{1} = - \frac{1}{3}, j_{2} = 0, j_{3} = \frac{1}{3}

Alternative Form

j_{1} = - 0. \dot{3}, j_{2} = 0, j_{3} = 0. \dot{3}

Evaluate

3 j^{2} \times 2 j^{2} \times 6 j^{2} - 4 j^{2} \times j^{2}

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

3 j^{2} \times 2 j^{2} \times 6 j^{2} - 4 j^{2} \times j^{2} = 0

Multiply

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Multiply the terms

3 j^{2} \times 2 j^{2} \times 6 j^{2}

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 6

Multiply the terms

6 \times 6

Multiply the numbers

36

36 j^{2} \times j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

36 j^{2 + 2 + 2}

Add the numbers

36 j^{6}

36 j^{6} - 4 j^{2} \times j^{2} = 0

Multiply

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Multiply the terms

4 j^{2} \times j^{2}

Multiply the terms with the same base by adding their exponents

4 j^{2 + 2}

Add the numbers

4 j^{4}

36 j^{6} - 4 j^{4} = 0

Factor the expression

4 j^{4} (9 j^{2} - 1) = 0

Divide both sides

j^{4} (9 j^{2} - 1) = 0

Separate the equation into 2 possible cases

j^{4} = 0 9 j^{2} - 1 = 0

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

j = 0 9 j^{2} - 1 = 0

Solve the equation

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Evaluate

9 j^{2} - 1 = 0

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

9 j^{2} = 0 + 1

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

9 j^{2} = 1

Divide both sides

\frac{9 j ^{2}}{9} = \frac{1}{9}

Divide the numbers

j^{2} = \frac{1}{9}

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

j = \pm \frac{1}{9}

Simplify the expression

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Evaluate

\frac{1}{9}

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

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

\frac{1}{3}

j = \pm \frac{1}{3}

Separate the equation into 2 possible cases

j = \frac{1}{3} j = - \frac{1}{3}

j = 0 j = \frac{1}{3} j = - \frac{1}{3}

Solution

j_{1} = - \frac{1}{3}, j_{2} = 0, j_{3} = \frac{1}{3}

Alternative Form

j_{1} = - 0. \dot{3}, j_{2} = 0, j_{3} = 0. \dot{3}

Show Solution