Solve a^2(3a-5)-(a^2 2)

Question

Simplify the expression

3 a^{3} - 7 a^{2}

Evaluate

a^{2} (3 a - 5) - (a^{2} \times 2)

Use the commutative property to reorder the terms

a^{2} (3 a - 5) - 2 a^{2}

Expand the expression

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Calculate

a^{2} (3 a - 5)

Apply the distributive property

a^{2} \times 3 a - a^{2} \times 5

Multiply the terms

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Evaluate

a^{2} \times 3 a

Use the commutative property to reorder the terms

3 a^{2} \times a

Multiply the terms

3 a^{3}

3 a^{3} - a^{2} \times 5

Use the commutative property to reorder the terms

3 a^{3} - 5 a^{2}

3 a^{3} - 5 a^{2} - 2 a^{2}

Solution

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Evaluate

- 5 a^{2} - 2 a^{2}

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

(- 5 - 2) a^{2}

Subtract the numbers

- 7 a^{2}

3 a^{3} - 7 a^{2}

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Factor the expression

a^{2} (3 a - 7)

Evaluate

a^{2} (3 a - 5) - (a^{2} \times 2)

Use the commutative property to reorder the terms

a^{2} (3 a - 5) - 2 a^{2}

Rewrite the expression

a^{2} (3 a - 5) - a^{2} \times 2

Factor out a^{2} from the expression

a^{2} (3 a - 5 - 2)

Solution

a^{2} (3 a - 7)

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Find the roots

a_{1} = 0, a_{2} = \frac{7}{3}

Alternative Form

a_{1} = 0, a_{2} = 2. \dot{3}

Evaluate

a^{2} (3 a - 5) - (a^{2} \times 2)

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

a^{2} (3 a - 5) - (a^{2} \times 2) = 0

Use the commutative property to reorder the terms

a^{2} (3 a - 5) - 2 a^{2} = 0

Calculate

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Evaluate

a^{2} (3 a - 5) - 2 a^{2}

Expand the expression

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Calculate

a^{2} (3 a - 5)

Apply the distributive property

a^{2} \times 3 a - a^{2} \times 5

Multiply the terms

3 a^{3} - a^{2} \times 5

Use the commutative property to reorder the terms

3 a^{3} - 5 a^{2}

3 a^{3} - 5 a^{2} - 2 a^{2}

Subtract the terms

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Evaluate

- 5 a^{2} - 2 a^{2}

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

(- 5 - 2) a^{2}

Subtract the numbers

- 7 a^{2}

3 a^{3} - 7 a^{2}

3 a^{3} - 7 a^{2} = 0

Factor the expression

a^{2} (3 a - 7) = 0

Separate the equation into 2 possible cases

a^{2} = 0 3 a - 7 = 0

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

a = 0 3 a - 7 = 0

Solve the equation

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Evaluate

3 a - 7 = 0

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

3 a = 0 + 7

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

3 a = 7

Divide both sides

\frac{3 a}{3} = \frac{7}{3}

Divide the numbers

a = \frac{7}{3}

a = 0 a = \frac{7}{3}

Solution

a_{1} = 0, a_{2} = \frac{7}{3}

Alternative Form

a_{1} = 0, a_{2} = 2. \dot{3}

Show Solution