Solve 33a^6a-33a - ScanMath

Question

Simplify the expression

33 a^{7} - 33 a

Evaluate

33 a^{6} \times a - 33 a

Solution

More Steps

Evaluate

33 a^{6} \times a

Multiply the terms with the same base by adding their exponents

33 a^{6 + 1}

Add the numbers

33 a^{7}

33 a^{7} - 33 a

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Factor the expression

33 a (a - 1) (a^{2} + a + 1) (a + 1) (a^{2} - a + 1)

Evaluate

33 a^{6} \times a - 33 a

Evaluate

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Evaluate

33 a^{6} \times a

Multiply the terms with the same base by adding their exponents

33 a^{6 + 1}

Add the numbers

33 a^{7}

33 a^{7} - 33 a

Factor out 33 a from the expression

33 a (a^{6} - 1)

Factor the expression

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Evaluate

a^{6} - 1

Rewrite the expression in exponential form

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

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

(a^{3} - 1) (a^{3} + 1)

33 a (a^{3} - 1) (a^{3} + 1)

Evaluate

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Evaluate

a^{3} - 1

Rewrite the expression in exponential form

a^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(a - 1) (a^{2} + a \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(a - 1) (a^{2} + a + 1^{2})

1 raised to any power equals to 1

(a - 1) (a^{2} + a + 1)

33 a (a - 1) (a^{2} + a + 1) (a^{3} + 1)

Solution

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Evaluate

a^{3} + 1

Rewrite the expression in exponential form

a^{3} + 1^{3}

Use a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) to factor the expression

(a + 1) (a^{2} - a \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(a + 1) (a^{2} - a + 1^{2})

1 raised to any power equals to 1

(a + 1) (a^{2} - a + 1)

33 a (a - 1) (a^{2} + a + 1) (a + 1) (a^{2} - a + 1)

Show Solution

Find the roots

a_{1} = - 1, a_{2} = 0, a_{3} = 1

Evaluate

33 a^{6} \times a - 33 a

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

33 a^{6} \times a - 33 a = 0

Multiply

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Multiply the terms

33 a^{6} \times a

Multiply the terms with the same base by adding their exponents

33 a^{6 + 1}

Add the numbers

33 a^{7}

33 a^{7} - 33 a = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

a^{6} - 1 = 0

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

a^{6} = 0 + 1

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

a^{6} = 1

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

a = \pm 61

Simplify the expression

a = \pm 1

Separate the equation into 2 possible cases

a = 1 a = - 1

a = 0 a = 1 a = - 1

Solution

a_{1} = - 1, a_{2} = 0, a_{3} = 1

Show Solution