Solve (2a 1)^2-4(a^2)(a-2)

Question

Simplify the expression

12 a^{2} - 4 a^{3}

Evaluate

(2 a \times 1)^{2} - 4 a^{2} (a - 2)

Multiply the terms

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

Rewrite the expression

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

Expand the expression

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Calculate

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

Apply the distributive property

- 4 a^{2} \times a - (- 4 a^{2} \times 2)

Multiply the terms

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Evaluate

a^{2} \times a

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

a^{2 + 1}

Add the numbers

a^{3}

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

Multiply the numbers

- 4 a^{3} - (- 8 a^{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

- 4 a^{3} + 8 a^{2}

4 a^{2} - 4 a^{3} + 8 a^{2}

Solution

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Evaluate

4 a^{2} + 8 a^{2}

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

(4 + 8) a^{2}

Add the numbers

12 a^{2}

12 a^{2} - 4 a^{3}

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Factor the expression

4 a^{2} (3 - a)

Evaluate

(2 a \times 1)^{2} - 4 a^{2} (a - 2)

Multiply the terms

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

Rewrite the expression

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

Factor out 4 a^{2} from the expression

4 a^{2} (1 - a + 2)

Solution

4 a^{2} (3 - a)

Show Solution

Find the roots

a_{1} = 0, a_{2} = 3

Evaluate

(2 a \times 1)^{2} - 4 (a^{2}) (a - 2)

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

(2 a \times 1)^{2} - 4 (a^{2}) (a - 2) = 0

Multiply the terms

(2 a)^{2} - 4 (a^{2}) (a - 2) = 0

Calculate

(2 a)^{2} - 4 a^{2} (a - 2) = 0

Rewrite the expression

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Simplify

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

Rewrite the expression

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Evaluate

(2 a)^{2}

To raise a product to a power,raise each factor to that power

2^{2} a^{2}

Evaluate the power

4 a^{2}

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

4 a^{2} - 4 a^{2} (a - 2) = 0

Calculate

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Evaluate

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

Expand the expression

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Calculate

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

Apply the distributive property

- 4 a^{2} \times a - (- 4 a^{2} \times 2)

Multiply the terms

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

Multiply the numbers

- 4 a^{3} - (- 8 a^{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

- 4 a^{3} + 8 a^{2}

4 a^{2} - 4 a^{3} + 8 a^{2}

Add the terms

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Evaluate

4 a^{2} + 8 a^{2}

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

(4 + 8) a^{2}

Add the numbers

12 a^{2}

12 a^{2} - 4 a^{3}

12 a^{2} - 4 a^{3} = 0

Factor the expression

4 a^{2} (3 - a) = 0

Divide both sides

a^{2} (3 - a) = 0

Separate the equation into 2 possible cases

a^{2} = 0 3 - a = 0

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

a = 0 3 - a = 0

Solve the equation

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Evaluate

3 - a = 0

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

- a = 0 - 3

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

- a = - 3

Change the signs on both sides of the equation

a = 3

a = 0 a = 3

Solution

a_{1} = 0, a_{2} = 3

Show Solution