Solve (16m^2 324-144m)(2m^2-6m 17)

Question

Simplify the expression

10368 m^{4} - 529056 m^{3} + 14688 m^{2}

Evaluate

(16 m^{2} \times 324 - 144 m) (2 m^{2} - 6 m \times 17)

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 6 m \times 17)

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 102 m)

Apply the distributive property

5184 m^{2} \times 2 m^{2} - 5184 m^{2} \times 102 m - 144 m \times 2 m^{2} - (- 144 m \times 102 m)

Multiply the terms

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Evaluate

5184 m^{2} \times 2 m^{2}

Multiply the numbers

10368 m^{2} \times m^{2}

Multiply the terms

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Evaluate

m^{2} \times m^{2}

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

m^{2 + 2}

Add the numbers

m^{4}

10368 m^{4}

10368 m^{4} - 5184 m^{2} \times 102 m - 144 m \times 2 m^{2} - (- 144 m \times 102 m)

Multiply the terms

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Evaluate

5184 m^{2} \times 102 m

Multiply the numbers

528768 m^{2} \times m

Multiply the terms

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Evaluate

m^{2} \times m

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

m^{2 + 1}

Add the numbers

m^{3}

528768 m^{3}

10368 m^{4} - 528768 m^{3} - 144 m \times 2 m^{2} - (- 144 m \times 102 m)

Multiply the terms

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Evaluate

- 144 m \times 2 m^{2}

Multiply the numbers

- 288 m \times m^{2}

Multiply the terms

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Evaluate

m \times m^{2}

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

m^{1 + 2}

Add the numbers

m^{3}

- 288 m^{3}

10368 m^{4} - 528768 m^{3} - 288 m^{3} - (- 144 m \times 102 m)

Multiply the terms

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Evaluate

- 144 m \times 102 m

Multiply the numbers

- 14688 m \times m

Multiply the terms

- 14688 m^{2}

10368 m^{4} - 528768 m^{3} - 288 m^{3} - (- 14688 m^{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

10368 m^{4} - 528768 m^{3} - 288 m^{3} + 14688 m^{2}

Solution

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Evaluate

- 528768 m^{3} - 288 m^{3}

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

(- 528768 - 288) m^{3}

Subtract the numbers

- 529056 m^{3}

10368 m^{4} - 529056 m^{3} + 14688 m^{2}

Show Solution

Factor the expression

288 m^{2} (36 m - 1) (m - 51)

Evaluate

(16 m^{2} \times 324 - 144 m) (2 m^{2} - 6 m \times 17)

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 6 m \times 17)

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 102 m)

Factor the expression

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Evaluate

5184 m^{2} - 144 m

Rewrite the expression

144 m \times 36 m - 144 m

Factor out 144 m from the expression

144 m (36 m - 1)

144 m (36 m - 1) (2 m^{2} - 102 m)

Factor the expression

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Evaluate

2 m^{2} - 102 m

Rewrite the expression

2 m \times m - 2 m \times 51

Factor out 2 m from the expression

2 m (m - 51)

144 m (36 m - 1) \times 2 m (m - 51)

Solution

288 m^{2} (36 m - 1) (m - 51)

Show Solution

Find the roots

m_{1} = 0, m_{2} = \frac{1}{36}, m_{3} = 51

Alternative Form

m_{1} = 0, m_{2} = 0.02 \dot{7}, m_{3} = 51

Evaluate

(16 m^{2} \times 324 - 144 m) (2 m^{2} - 6 m \times 17)

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

(16 m^{2} \times 324 - 144 m) (2 m^{2} - 6 m \times 17) = 0

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 6 m \times 17) = 0

Multiply the terms

(5184 m^{2} - 144 m) (2 m^{2} - 102 m) = 0

Separate the equation into 2 possible cases

5184 m^{2} - 144 m = 0 2 m^{2} - 102 m = 0

Solve the equation

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Evaluate

5184 m^{2} - 144 m = 0

Factor the expression

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Evaluate

5184 m^{2} - 144 m

Rewrite the expression

144 m \times 36 m - 144 m

Factor out 144 m from the expression

144 m (36 m - 1)

144 m (36 m - 1) = 0

When the product of factors equals 0,at least one factor is 0

144 m = 0 36 m - 1 = 0

Solve the equation for m

m = 0 36 m - 1 = 0

Solve the equation for m

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Evaluate

36 m - 1 = 0

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

36 m = 0 + 1

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

36 m = 1

Divide both sides

\frac{36 m}{36} = \frac{1}{36}

Divide the numbers

m = \frac{1}{36}

m = 0 m = \frac{1}{36}

m = 0 m = \frac{1}{36} 2 m^{2} - 102 m = 0

Solve the equation

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Evaluate

2 m^{2} - 102 m = 0

Factor the expression

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Evaluate

2 m^{2} - 102 m

Rewrite the expression

2 m \times m - 2 m \times 51

Factor out 2 m from the expression

2 m (m - 51)

2 m (m - 51) = 0

When the product of factors equals 0,at least one factor is 0

2 m = 0 m - 51 = 0

Solve the equation for m

m = 0 m - 51 = 0

Solve the equation for m

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Evaluate

m - 51 = 0

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

m = 0 + 51

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

m = 51

m = 0 m = 51

m = 0 m = \frac{1}{36} m = 0 m = 51

Find the union

m = 0 m = \frac{1}{36} m = 51

Solution

m_{1} = 0, m_{2} = \frac{1}{36}, m_{3} = 51

Alternative Form

m_{1} = 0, m_{2} = 0.02 \dot{7}, m_{3} = 51

Show Solution