Solve (y^3)(10y-6)-(8y-4)(1)

Question

Simplify the expression

10 y^{4} - 6 y^{3} - 8 y + 4

Evaluate

y^{3} (10 y - 6) - (8 y - 4) \times 1

Any expression multiplied by 1 remains the same

y^{3} (10 y - 6) - (8 y - 4)

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

y^{3} (10 y - 6) - 8 y + 4

Solution

More Steps

Evaluate

y^{3} (10 y - 6)

Apply the distributive property

y^{3} \times 10 y - y^{3} \times 6

Multiply the terms

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Evaluate

y^{3} \times 10 y

Use the commutative property to reorder the terms

10 y^{3} \times y

Multiply the terms

10 y^{4}

10 y^{4} - y^{3} \times 6

Use the commutative property to reorder the terms

10 y^{4} - 6 y^{3}

10 y^{4} - 6 y^{3} - 8 y + 4

Show Solution

Factor the expression

2 (y - 1) (5 y^{3} + 2 y^{2} + 2 y - 2)

Evaluate

y^{3} (10 y - 6) - (8 y - 4) \times 1

Multiply the terms

y^{3} (10 y - 6) - (8 y - 4)

Simplify

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Evaluate

y^{3} (10 y - 6)

Apply the distributive property

y^{3} \times 10 y + y^{3} (- 6)

Multiply the terms

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Evaluate

y^{3} \times 10 y

Use the commutative property to reorder the terms

10 y^{3} \times y

Multiply the terms

10 y^{4}

10 y^{4} + y^{3} (- 6)

Use the commutative property to reorder the terms

10 y^{4} - 6 y^{3}

10 y^{4} - 6 y^{3} - (8 y - 4)

Simplify

10 y^{4} - 6 y^{3} - 8 y + 4

Rewrite the expression

2 \times 5 y^{4} - 2 \times 3 y^{3} - 2 \times 4 y + 2 \times 2

Factor out 2 from the expression

2 (5 y^{4} - 3 y^{3} - 4 y + 2)

Solution

More Steps

Evaluate

5 y^{4} - 3 y^{3} - 4 y + 2

Calculate

5 y^{4} + 2 y^{3} + 2 y^{2} - 2 y - 5 y^{3} - 2 y^{2} - 2 y + 2

Rewrite the expression

y \times 5 y^{3} + y \times 2 y^{2} + y \times 2 y - y \times 2 - 5 y^{3} - 2 y^{2} - 2 y + 2

Factor out y from the expression

y (5 y^{3} + 2 y^{2} + 2 y - 2) - 5 y^{3} - 2 y^{2} - 2 y + 2

Factor out - 1 from the expression

y (5 y^{3} + 2 y^{2} + 2 y - 2) - (5 y^{3} + 2 y^{2} + 2 y - 2)

Factor out 5 y^{3} + 2 y^{2} + 2 y - 2 from the expression

(y - 1) (5 y^{3} + 2 y^{2} + 2 y - 2)

2 (y - 1) (5 y^{3} + 2 y^{2} + 2 y - 2)

Show Solution

Find the roots

y_{1} \approx 0.483542, y_{2} = 1

Evaluate

(y^{3}) (10 y - 6) - (8 y - 4) \times 1

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

(y^{3}) (10 y - 6) - (8 y - 4) \times 1 = 0

Calculate

y^{3} (10 y - 6) - (8 y - 4) \times 1 = 0

Any expression multiplied by 1 remains the same

y^{3} (10 y - 6) - (8 y - 4) = 0

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

y^{3} (10 y - 6) - 8 y + 4 = 0

Calculate

More Steps

Evaluate

y^{3} (10 y - 6)

Apply the distributive property

y^{3} \times 10 y - y^{3} \times 6

Multiply the terms

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Evaluate

y^{3} \times 10 y

Use the commutative property to reorder the terms

10 y^{3} \times y

Multiply the terms

10 y^{4}

10 y^{4} - y^{3} \times 6

Use the commutative property to reorder the terms

10 y^{4} - 6 y^{3}

10 y^{4} - 6 y^{3} - 8 y + 4 = 0

Factor the expression

2 (y - 1) (5 y^{3} + 2 y^{2} + 2 y - 2) = 0

Divide both sides

(y - 1) (5 y^{3} + 2 y^{2} + 2 y - 2) = 0

Separate the equation into 2 possible cases

y - 1 = 0 5 y^{3} + 2 y^{2} + 2 y - 2 = 0

Solve the equation

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Evaluate

y - 1 = 0

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

y = 0 + 1

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

y = 1

y = 1 5 y^{3} + 2 y^{2} + 2 y - 2 = 0

Solve the equation

y = 1 y \approx 0.483542

Solution

y_{1} \approx 0.483542, y_{2} = 1

Show Solution