Solve (8m^26m 8)-(4m^26)

Question

Simplify the expression

384 m^{3} - 24 m^{2}

Evaluate

(8 m^{2} \times 6 m \times 8) - (4 m^{2} \times 6)

Multiply

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Multiply the terms

8 m^{2} \times 6 m \times 8

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

384 m^{2} \times m

Multiply the terms with the same base by adding their exponents

384 m^{2 + 1}

Add the numbers

384 m^{3}

384 m^{3} - (4 m^{2} \times 6)

Solution

384 m^{3} - 24 m^{2}

Show Solution

Factor the expression

24 m^{2} (16 m - 1)

Evaluate

(8 m^{2} \times 6 m \times 8) - (4 m^{2} \times 6)

Multiply

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Multiply the terms

8 m^{2} \times 6 m \times 8

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

384 m^{2} \times m

Multiply the terms with the same base by adding their exponents

384 m^{2 + 1}

Add the numbers

384 m^{3}

384 m^{3} - (4 m^{2} \times 6)

Multiply the terms

384 m^{3} - 24 m^{2}

Rewrite the expression

24 m^{2} \times 16 m - 24 m^{2}

Solution

24 m^{2} (16 m - 1)

Show Solution

Find the roots

m_{1} = 0, m_{2} = \frac{1}{16}

Alternative Form

m_{1} = 0, m_{2} = 0.0625

Evaluate

(8 m^{2} \times 6 m \times 8) - (4 m^{2} \times 6)

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

(8 m^{2} \times 6 m \times 8) - (4 m^{2} \times 6) = 0

Multiply

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Multiply the terms

8 m^{2} \times 6 m \times 8

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

384 m^{2} \times m

Multiply the terms with the same base by adding their exponents

384 m^{2 + 1}

Add the numbers

384 m^{3}

384 m^{3} - (4 m^{2} \times 6) = 0

Multiply the terms

384 m^{3} - 24 m^{2} = 0

Factor the expression

24 m^{2} (16 m - 1) = 0

Divide both sides

m^{2} (16 m - 1) = 0

Separate the equation into 2 possible cases

m^{2} = 0 16 m - 1 = 0

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

m = 0 16 m - 1 = 0

Solve the equation

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Evaluate

16 m - 1 = 0

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

16 m = 0 + 1

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

16 m = 1

Divide both sides

\frac{16 m}{16} = \frac{1}{16}

Divide the numbers

m = \frac{1}{16}

m = 0 m = \frac{1}{16}

Solution

m_{1} = 0, m_{2} = \frac{1}{16}

Alternative Form

m_{1} = 0, m_{2} = 0.0625

Show Solution