Solve 40g^5 24g^3-12g^2-20g^4

Question

Simplify the expression

960 g^{8} - 12 g^{2} - 20 g^{4}

Evaluate

40 g^{5} \times 24 g^{3} - 12 g^{2} - 20 g^{4}

Solution

More Steps

Evaluate

40 g^{5} \times 24 g^{3}

Multiply the terms

960 g^{5} \times g^{3}

Multiply the terms with the same base by adding their exponents

960 g^{5 + 3}

Add the numbers

960 g^{8}

960 g^{8} - 12 g^{2} - 20 g^{4}

Show Solution

4 g^{2} (240 g^{6} - 3 - 5 g^{2})

Evaluate

40 g^{5} \times 24 g^{3} - 12 g^{2} - 20 g^{4}

Multiply

More Steps

Evaluate

40 g^{5} \times 24 g^{3}

Multiply the terms

960 g^{5} \times g^{3}

Multiply the terms with the same base by adding their exponents

960 g^{5 + 3}

Add the numbers

960 g^{8}

960 g^{8} - 12 g^{2} - 20 g^{4}

Rewrite the expression

4 g^{2} \times 240 g^{6} - 4 g^{2} \times 3 - 4 g^{2} \times 5 g^{2}

Solution

4 g^{2} (240 g^{6} - 3 - 5 g^{2})

Show Solution

g_{1} \approx - 0.51172, g_{2} = 0, g_{3} \approx 0.51172

Evaluate

40 g^{5} \times 24 g^{3} - 12 g^{2} - 20 g^{4}

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

40 g^{5} \times 24 g^{3} - 12 g^{2} - 20 g^{4} = 0

Multiply

More Steps

Multiply the terms

40 g^{5} \times 24 g^{3}

Multiply the terms

960 g^{5} \times g^{3}

Multiply the terms with the same base by adding their exponents

960 g^{5 + 3}

Add the numbers

960 g^{8}

960 g^{8} - 12 g^{2} - 20 g^{4} = 0

Factor the expression

4 g^{2} (240 g^{6} - 3 - 5 g^{2}) = 0

Divide both sides

g^{2} (240 g^{6} - 3 - 5 g^{2}) = 0

Separate the equation into 2 possible cases

g^{2} = 0 240 g^{6} - 3 - 5 g^{2} = 0

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

g = 0 240 g^{6} - 3 - 5 g^{2} = 0

Solve the equation

More Steps

Evaluate

240 g^{6} - 3 - 5 g^{2} = 0

Solve the equation using substitution t = g^{2}

240 t^{3} - 3 - 5 t = 0

Calculate

t \approx 0.261857

Substitute back

g^{2} \approx 0.261857

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

g = \pm 0.261857

Simplify the expression

g = \pm 0.51172

Separate the equation into 2 possible cases

g \approx 0.51172 g \approx - 0.51172

g = 0 g \approx 0.51172 g \approx - 0.51172

Solution

g_{1} \approx - 0.51172, g_{2} = 0, g_{3} \approx 0.51172

Show Solution