Solve 4m^2 2m 8m-9 3m^2 4

Question

Simplify the expression

64 m^{4} - 372 m^{2}

Evaluate

4 m^{2} \times 2 m \times 8 m - 93 m^{2} \times 4

Multiply

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Multiply the terms

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

Multiply the terms

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Evaluate

4 \times 2 \times 8

Multiply the terms

8 \times 8

Multiply the numbers

64

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

Multiply the terms with the same base by adding their exponents

64 m^{2 + 1 + 1}

Add the numbers

64 m^{4}

64 m^{4} - 93 m^{2} \times 4

Solution

64 m^{4} - 372 m^{2}

Show Solution

Factor the expression

4 m^{2} (16 m^{2} - 93)

Evaluate

4 m^{2} \times 2 m \times 8 m - 93 m^{2} \times 4

Multiply

More Steps

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

4 \times 2 \times 8

Multiply the terms

8 \times 8

Multiply the numbers

64

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

Multiply the terms with the same base by adding their exponents

64 m^{2 + 1 + 1}

Add the numbers

64 m^{4}

64 m^{4} - 93 m^{2} \times 4

Multiply the terms

64 m^{4} - 372 m^{2}

Rewrite the expression

4 m^{2} \times 16 m^{2} - 4 m^{2} \times 93

Solution

4 m^{2} (16 m^{2} - 93)

Show Solution

Find the roots

m_{1} = - \frac{93}{4}, m_{2} = 0, m_{3} = \frac{93}{4}

Alternative Form

m_{1} \approx - 2.410913, m_{2} = 0, m_{3} \approx 2.410913

Evaluate

4 m^{2} \times 2 m \times 8 m - 93 m^{2} \times 4

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

4 m^{2} \times 2 m \times 8 m - 93 m^{2} \times 4 = 0

Multiply

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Multiply the terms

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

Multiply the terms

More Steps

Evaluate

4 \times 2 \times 8

Multiply the terms

8 \times 8

Multiply the numbers

64

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

Multiply the terms with the same base by adding their exponents

64 m^{2 + 1 + 1}

Add the numbers

64 m^{4}

64 m^{4} - 93 m^{2} \times 4 = 0

Multiply the terms

64 m^{4} - 372 m^{2} = 0

Factor the expression

4 m^{2} (16 m^{2} - 93) = 0

Divide both sides

m^{2} (16 m^{2} - 93) = 0

Separate the equation into 2 possible cases

m^{2} = 0 16 m^{2} - 93 = 0

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

m = 0 16 m^{2} - 93 = 0

Solve the equation

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Evaluate

16 m^{2} - 93 = 0

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

16 m^{2} = 0 + 93

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

16 m^{2} = 93

Divide both sides

\frac{16 m ^{2}}{16} = \frac{93}{16}

Divide the numbers

m^{2} = \frac{93}{16}

Take the root of both sides of the equation and remember to use both positive and negative roots

m = \pm \frac{93}{16}

Simplify the expression

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Evaluate

\frac{93}{16}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{93}{16}

Simplify the radical expression

\frac{93}{4}

m = \pm \frac{93}{4}

Separate the equation into 2 possible cases

m = \frac{93}{4} m = - \frac{93}{4}

m = 0 m = \frac{93}{4} m = - \frac{93}{4}

Solution

m_{1} = - \frac{93}{4}, m_{2} = 0, m_{3} = \frac{93}{4}

Alternative Form

m_{1} \approx - 2.410913, m_{2} = 0, m_{3} \approx 2.410913

Show Solution