Solve 5(k-1)^(2) 3(k-1)-6

Question

Simplify the expression

15 k^{3} - 45 k^{2} + 45 k - 21

Evaluate

5 (k - 1)^{2} \times 3 (k - 1) - 6

Multiply

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Multiply the terms

5 (k - 1)^{2} \times 3 (k - 1)

Multiply the terms

15 (k - 1)^{2} (k - 1)

Multiply the terms with the same base by adding their exponents

15 (k - 1)^{2 + 1}

Add the numbers

15 (k - 1)^{3}

15 (k - 1)^{3} - 6

Expand the expression

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Calculate

15 (k - 1)^{3}

Simplify

15 (k^{3} - 3 k^{2} + 3 k - 1)

Apply the distributive property

15 k^{3} - 15 \times 3 k^{2} + 15 \times 3 k - 15 \times 1

Multiply the numbers

15 k^{3} - 45 k^{2} + 15 \times 3 k - 15 \times 1

Multiply the numbers

15 k^{3} - 45 k^{2} + 45 k - 15 \times 1

Any expression multiplied by 1 remains the same

15 k^{3} - 45 k^{2} + 45 k - 15

15 k^{3} - 45 k^{2} + 45 k - 15 - 6

Solution

15 k^{3} - 45 k^{2} + 45 k - 21

Show Solution

Factor the expression

3 (5 k^{3} - 15 k^{2} + 15 k - 7)

Evaluate

5 (k - 1)^{2} \times 3 (k - 1) - 6

Multiply

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Evaluate

5 (k - 1)^{2} \times 3 (k - 1)

Multiply the terms

15 (k - 1)^{2} (k - 1)

Multiply the terms with the same base by adding their exponents

15 (k - 1)^{2 + 1}

Add the numbers

15 (k - 1)^{3}

15 (k - 1)^{3} - 6

Simplify

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Evaluate

15 (k - 1)^{3}

Simplify

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Evaluate

(k - 1)^{3}

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

k^{3} - 3 k^{2} \times 1 + 3 k \times 1^{2} - 1^{3}

Calculate

k^{3} - 3 k^{2} + 3 k - 1

15 (k^{3} - 3 k^{2} + 3 k - 1)

Apply the distributive property

15 k^{3} + 15 (- 3 k^{2}) + 15 \times 3 k + 15 (- 1)

Multiply the terms

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Evaluate

15 (- 3)

Multiplying or dividing an odd number of negative terms equals a negative

- 15 \times 3

Multiply the numbers

- 45

15 k^{3} - 45 k^{2} + 15 \times 3 k + 15 (- 1)

Multiply the terms

15 k^{3} - 45 k^{2} + 45 k + 15 (- 1)

Multiply the terms

15 k^{3} - 45 k^{2} + 45 k - 15

15 k^{3} - 45 k^{2} + 45 k - 15 - 6

Subtract the numbers

15 k^{3} - 45 k^{2} + 45 k - 21

Solution

3 (5 k^{3} - 15 k^{2} + 15 k - 7)

Show Solution

Find the roots

k = \frac{3 50 + 5}{5}

Alternative Form

k \approx 1.736806

Evaluate

5 (k - 1)^{2} \times 3 (k - 1) - 6

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

5 (k - 1)^{2} \times 3 (k - 1) - 6 = 0

Multiply

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Multiply the terms

5 (k - 1)^{2} \times 3 (k - 1)

Multiply the terms

15 (k - 1)^{2} (k - 1)

Multiply the terms with the same base by adding their exponents

15 (k - 1)^{2 + 1}

Add the numbers

15 (k - 1)^{3}

15 (k - 1)^{3} - 6 = 0

Add or subtract both sides

15 (k - 1)^{3} = 0 + 6

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

15 (k - 1)^{3} = 6

Divide both sides

\frac{15 ( k - 1 ) ^{3}}{15} = \frac{6}{15}

Divide the numbers

(k - 1)^{3} = \frac{6}{15}

Cancel out the common factor 3

(k - 1)^{3} = \frac{2}{5}

Take the 3 -th root on both sides of the equation

3 (k - 1)^{3} = 3 \frac{2}{5}

Calculate

k - 1 = 3 \frac{2}{5}

Simplify the root

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Evaluate

3 \frac{2}{5}

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

\frac{3 2}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{3 2 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

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Evaluate

32 \times 325

The product of roots with the same index is equal to the root of the product

3 2 \times 25

Calculate the product

350

\frac{3 50}{3 5 \times 3 5 ^{2}}

Multiply the numbers

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Evaluate

35 \times 3 5^{2}

The product of roots with the same index is equal to the root of the product

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 50}{5}

k - 1 = \frac{3 50}{5}

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

k = \frac{3 50}{5} + 1

Solution

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Evaluate

\frac{3 50}{5} + 1

Reduce fractions to a common denominator

\frac{3 50}{5} + \frac{5}{5}

Write all numerators above the common denominator

\frac{3 50 + 5}{5}

k = \frac{3 50 + 5}{5}

Alternative Form

k \approx 1.736806

Show Solution