Solve 81a^4-256 - ScanMath

Question

81 a^{4} - 256

Factor the expression

(3 a - 4) (3 a + 4) (9 a^{2} + 16)

Evaluate

81 a^{4} - 256

Rewrite the expression in exponential form

(9 a^{2})^{2} - (25 6^{\frac{1}{2}})^{2}

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

(9 a^{2} - 25 6^{\frac{1}{2}}) (9 a^{2} + 25 6^{\frac{1}{2}})

Evaluate

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Evaluate

9 a^{2} - 25 6^{\frac{1}{2}}

Calculate

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Evaluate

- 25 6^{\frac{1}{2}}

Rewrite in exponential form

- (2^{8})^{\frac{1}{2}}

Multiply the exponents

- 2^{8 \times \frac{1}{2}}

Multiply the exponents

- 2^{4}

Evaluate the power

- 16

9 a^{2} - 16

(9 a^{2} - 16) (9 a^{2} + 25 6^{\frac{1}{2}})

Evaluate

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Evaluate

9 a^{2} + 25 6^{\frac{1}{2}}

Calculate

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Evaluate

25 6^{\frac{1}{2}}

Rewrite in exponential form

(2^{8})^{\frac{1}{2}}

Multiply the exponents

2^{8 \times \frac{1}{2}}

Multiply the exponents

2^{4}

Evaluate the power

16

9 a^{2} + 16

(9 a^{2} - 16) (9 a^{2} + 16)

Solution

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Evaluate

9 a^{2} - 16

Rewrite the expression in exponential form

(3 a)^{2} - 4^{2}

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

(3 a - 4) (3 a + 4)

(3 a - 4) (3 a + 4) (9 a^{2} + 16)

Show Solution

Find the roots

a_{1} = - \frac{4}{3}, a_{2} = \frac{4}{3}

Alternative Form

a_{1} = - 1. \dot{3}, a_{2} = 1. \dot{3}

Evaluate

81 a^{4} - 256

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

81 a^{4} - 256 = 0

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

81 a^{4} = 0 + 256

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

81 a^{4} = 256

Divide both sides

\frac{81 a ^{4}}{81} = \frac{256}{81}

Divide the numbers

a^{4} = \frac{256}{81}

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

a = \pm 4 \frac{256}{81}

Simplify the expression

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Evaluate

4 \frac{256}{81}

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

\frac{4 256}{4 81}

Simplify the radical expression

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Evaluate

4256

Write the number in exponential form with the base of 4

4 4^{4}

Reduce the index of the radical and exponent with 4

4

\frac{4}{4 81}

Simplify the radical expression

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Evaluate

481

Write the number in exponential form with the base of 3

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4}{3}

a = \pm \frac{4}{3}

Separate the equation into 2 possible cases

a = \frac{4}{3} a = - \frac{4}{3}

Solution

a_{1} = - \frac{4}{3}, a_{2} = \frac{4}{3}

Alternative Form

a_{1} = - 1. \dot{3}, a_{2} = 1. \dot{3}

Show Solution