Solve 39y^(5) 12y^(4)-3y^(3)

Question

Simplify the expression

468 y^{9} - 3 y^{3}

Evaluate

39 y^{5} \times 12 y^{4} - 3 y^{3}

Solution

More Steps

Evaluate

39 y^{5} \times 12 y^{4}

Multiply the terms

468 y^{5} \times y^{4}

Multiply the terms with the same base by adding their exponents

468 y^{5 + 4}

Add the numbers

468 y^{9}

468 y^{9} - 3 y^{3}

Show Solution

Factor the expression

3 y^{3} (156 y^{6} - 1)

Evaluate

39 y^{5} \times 12 y^{4} - 3 y^{3}

Multiply

More Steps

Evaluate

39 y^{5} \times 12 y^{4}

Multiply the terms

468 y^{5} \times y^{4}

Multiply the terms with the same base by adding their exponents

468 y^{5 + 4}

Add the numbers

468 y^{9}

468 y^{9} - 3 y^{3}

Rewrite the expression

3 y^{3} \times 156 y^{6} - 3 y^{3}

Solution

3 y^{3} (156 y^{6} - 1)

Show Solution

Find the roots

y_{1} = - \frac{6 15 6 ^{5}}{156}, y_{2} = 0, y_{3} = \frac{6 15 6 ^{5}}{156}

Alternative Form

y_{1} \approx - 0.431002, y_{2} = 0, y_{3} \approx 0.431002

Evaluate

39 y^{5} \times 12 y^{4} - 3 y^{3}

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

39 y^{5} \times 12 y^{4} - 3 y^{3} = 0

Multiply

More Steps

Multiply the terms

39 y^{5} \times 12 y^{4}

Multiply the terms

468 y^{5} \times y^{4}

Multiply the terms with the same base by adding their exponents

468 y^{5 + 4}

Add the numbers

468 y^{9}

468 y^{9} - 3 y^{3} = 0

Factor the expression

3 y^{3} (156 y^{6} - 1) = 0

Divide both sides

y^{3} (156 y^{6} - 1) = 0

Separate the equation into 2 possible cases

y^{3} = 0 156 y^{6} - 1 = 0

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

y = 0 156 y^{6} - 1 = 0

Solve the equation

More Steps

Evaluate

156 y^{6} - 1 = 0

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

156 y^{6} = 0 + 1

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

156 y^{6} = 1

Divide both sides

\frac{156 y ^{6}}{156} = \frac{1}{156}

Divide the numbers

y^{6} = \frac{1}{156}

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

y = \pm 6 \frac{1}{156}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{156}

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

\frac{6 1}{6 156}

Simplify the radical expression

\frac{1}{6 156}

Multiply by the Conjugate

\frac{6 15 6 ^{5}}{6 156 \times 6 15 6 ^{5}}

Multiply the numbers

\frac{6 15 6 ^{5}}{156}

y = \pm \frac{6 15 6 ^{5}}{156}

Separate the equation into 2 possible cases

y = \frac{6 15 6 ^{5}}{156} y = - \frac{6 15 6 ^{5}}{156}

y = 0 y = \frac{6 15 6 ^{5}}{156} y = - \frac{6 15 6 ^{5}}{156}

Solution

y_{1} = - \frac{6 15 6 ^{5}}{156}, y_{2} = 0, y_{3} = \frac{6 15 6 ^{5}}{156}

Alternative Form

y_{1} \approx - 0.431002, y_{2} = 0, y_{3} \approx 0.431002

Show Solution