Solve 7y^2 - 2[3(2y - 4) 3(2y^2)]

Question

Simplify the expression

151 y^{2} - 72 y^{3}

Evaluate

7 y^{2} - 2 (3 (2 y - 4) \times 3 \times 2 y^{2})

Remove the parentheses

7 y^{2} - 2 \times 3 (2 y - 4) \times 3 \times 2 y^{2}

Multiply

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Multiply the terms

2 \times 3 (2 y - 4) \times 3 \times 2 y^{2}

Multiply the terms

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Evaluate

2 \times 3 \times 3 \times 2

Multiply the terms

6 \times 3 \times 2

Multiply the terms

18 \times 2

Multiply the numbers

36

36 (2 y - 4) y^{2}

Multiply the terms

36 y^{2} (2 y - 4)

7 y^{2} - 36 y^{2} (2 y - 4)

Expand the expression

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Calculate

- 36 y^{2} (2 y - 4)

Apply the distributive property

- 36 y^{2} \times 2 y - (- 36 y^{2} \times 4)

Multiply the terms

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Evaluate

- 36 y^{2} \times 2 y

Multiply the numbers

- 72 y^{2} \times y

Multiply the terms

- 72 y^{3}

- 72 y^{3} - (- 36 y^{2} \times 4)

Multiply the numbers

- 72 y^{3} - (- 144 y^{2})

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

- 72 y^{3} + 144 y^{2}

7 y^{2} - 72 y^{3} + 144 y^{2}

Solution

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Evaluate

7 y^{2} + 144 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(7 + 144) y^{2}

Add the numbers

151 y^{2}

151 y^{2} - 72 y^{3}

Show Solution

Factor the expression

(151 - 72 y) y^{2}

Evaluate

7 y^{2} - 2 (3 (2 y - 4) \times 3 \times 2 y^{2})

Remove the parentheses

7 y^{2} - 2 \times 3 (2 y - 4) \times 3 \times 2 y^{2}

Multiply

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Multiply the terms

3 (2 y - 4) \times 3 \times 2 y^{2}

Multiply the terms

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Evaluate

3 \times 3 \times 2

Multiply the terms

9 \times 2

Multiply the numbers

18

18 (2 y - 4) y^{2}

Multiply the terms

18 y^{2} (2 y - 4)

7 y^{2} - 2 \times 18 y^{2} (2 y - 4)

Calculate

7 y^{2} - 36 y^{2} (2 y - 4)

Rewrite the expression

7 y^{2} - 72 (y - 2) y^{2}

Factor out y^{2} from the expression

(7 - 72 (y - 2)) y^{2}

Solution

(151 - 72 y) y^{2}

Show Solution

Find the roots

y_{1} = 0, y_{2} = \frac{151}{72}

Alternative Form

y_{1} = 0, y_{2} = 2.097 \dot{2}

Evaluate

7 y^{2} - 2 (3 (2 y - 4) \times 3 (2 y^{2}))

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

7 y^{2} - 2 (3 (2 y - 4) \times 3 (2 y^{2})) = 0

Multiply the terms

7 y^{2} - 2 (3 (2 y - 4) \times 3 \times 2 y^{2}) = 0

Multiply

More Steps

Multiply the terms

3 (2 y - 4) \times 3 \times 2 y^{2}

Multiply the terms

More Steps

Evaluate

3 \times 3 \times 2

Multiply the terms

9 \times 2

Multiply the numbers

18

18 (2 y - 4) y^{2}

Multiply the terms

18 y^{2} (2 y - 4)

7 y^{2} - 2 \times 18 y^{2} (2 y - 4) = 0

Multiply the terms

7 y^{2} - 36 y^{2} (2 y - 4) = 0

Calculate

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Evaluate

7 y^{2} - 36 y^{2} (2 y - 4)

Expand the expression

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Calculate

- 36 y^{2} (2 y - 4)

Apply the distributive property

- 36 y^{2} \times 2 y - (- 36 y^{2} \times 4)

Multiply the terms

- 72 y^{3} - (- 36 y^{2} \times 4)

Multiply the numbers

- 72 y^{3} - (- 144 y^{2})

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

- 72 y^{3} + 144 y^{2}

7 y^{2} - 72 y^{3} + 144 y^{2}

Add the terms

More Steps

Evaluate

7 y^{2} + 144 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(7 + 144) y^{2}

Add the numbers

151 y^{2}

151 y^{2} - 72 y^{3}

151 y^{2} - 72 y^{3} = 0

Factor the expression

y^{2} (151 - 72 y) = 0

Separate the equation into 2 possible cases

y^{2} = 0 151 - 72 y = 0

The only way a power can be 0 is when the base equals 0

y = 0 151 - 72 y = 0

Solve the equation

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Evaluate

151 - 72 y = 0

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

- 72 y = 0 - 151

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

- 72 y = - 151

Change the signs on both sides of the equation

72 y = 151

Divide both sides

\frac{72 y}{72} = \frac{151}{72}

Divide the numbers

y = \frac{151}{72}

y = 0 y = \frac{151}{72}

Solution

y_{1} = 0, y_{2} = \frac{151}{72}

Alternative Form

y_{1} = 0, y_{2} = 2.097 \dot{2}

Show Solution