Solve (y - 17)^2 (y-1)(7y - 71)

Question

Simplify the expression

7 y^{4} - 316 y^{3} + 4746 y^{2} - 24956 y + 20519

Evaluate

(y - 17)^{2} (y - 1) (7 y - 71)

Expand the expression

More Steps

(y^{2} - 34 y + 289) (y - 1) (7 y - 71)

Multiply the terms

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(y^{3} - 35 y^{2} + 323 y - 289) (7 y - 71)

Apply the distributive property

y^{3} \times 7 y - y^{3} \times 71 - 35 y^{2} \times 7 y - (- 35 y^{2} \times 71) + 323 y \times 7 y - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Multiply the terms

More Steps

7 y^{4} - y^{3} \times 71 - 35 y^{2} \times 7 y - (- 35 y^{2} \times 71) + 323 y \times 7 y - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Use the commutative property to reorder the terms

7 y^{4} - 71 y^{3} - 35 y^{2} \times 7 y - (- 35 y^{2} \times 71) + 323 y \times 7 y - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Multiply the terms

More Steps

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 35 y^{2} \times 71) + 323 y \times 7 y - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Multiply the numbers

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 2485 y^{2}) + 323 y \times 7 y - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Multiply the terms

More Steps

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 2485 y^{2}) + 2261 y^{2} - 323 y \times 71 - 289 \times 7 y - (- 289 \times 71)

Multiply the numbers

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 2485 y^{2}) + 2261 y^{2} - 22933 y - 289 \times 7 y - (- 289 \times 71)

Multiply the numbers

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 2485 y^{2}) + 2261 y^{2} - 22933 y - 2023 y - (- 289 \times 71)

Multiply the numbers

7 y^{4} - 71 y^{3} - 245 y^{3} - (- 2485 y^{2}) + 2261 y^{2} - 22933 y - 2023 y - (- 20519)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

7 y^{4} - 71 y^{3} - 245 y^{3} + 2485 y^{2} + 2261 y^{2} - 22933 y - 2023 y + 20519

Subtract the terms

More Steps

7 y^{4} - 316 y^{3} + 2485 y^{2} + 2261 y^{2} - 22933 y - 2023 y + 20519

Add the terms

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7 y^{4} - 316 y^{3} + 4746 y^{2} - 22933 y - 2023 y + 20519

Solution

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7 y^{4} - 316 y^{3} + 4746 y^{2} - 24956 y + 20519

Show Solution

Find the roots

y_{1} = 1, y_{2} = \frac{71}{7}, y_{3} = 17

Alternative Form

y_{1} = 1, y_{2} = 10. \dot{1} 4285 \dot{7}, y_{3} = 17

Show Solution