Solve 45y-22y^34y-23y

Question

Simplify the expression

22 y - 88 y^{4}

Evaluate

45 y - 22 y^{3} \times 4 y - 23 y

Multiply

More Steps

Multiply the terms

- 22 y^{3} \times 4 y

Multiply the terms

- 88 y^{3} \times y

Multiply the terms with the same base by adding their exponents

- 88 y^{3 + 1}

Add the numbers

- 88 y^{4}

45 y - 88 y^{4} - 23 y

Solution

More Steps

Evaluate

45 y - 23 y

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

(45 - 23) y

Subtract the numbers

22 y

22 y - 88 y^{4}

Show Solution

Factor the expression

22 y (1 - 4 y^{3})

Evaluate

45 y - 22 y^{3} \times 4 y - 23 y

Multiply

More Steps

Multiply the terms

22 y^{3} \times 4 y

Multiply the terms

88 y^{3} \times y

Multiply the terms with the same base by adding their exponents

88 y^{3 + 1}

Add the numbers

88 y^{4}

45 y - 88 y^{4} - 23 y

Subtract the terms

More Steps

Evaluate

45 y - 23 y

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

(45 - 23) y

Subtract the numbers

22 y

22 y - 88 y^{4}

Rewrite the expression

22 y - 22 y \times 4 y^{3}

Solution

22 y (1 - 4 y^{3})

Show Solution

Find the roots

y_{1} = 0, y_{2} = \frac{3 2}{2}

Alternative Form

y_{1} = 0, y_{2} \approx 0.629961

Evaluate

45 y - 22 y^{3} \times 4 y - 23 y

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

45 y - 22 y^{3} \times 4 y - 23 y = 0

Multiply

More Steps

Multiply the terms

22 y^{3} \times 4 y

Multiply the terms

88 y^{3} \times y

Multiply the terms with the same base by adding their exponents

88 y^{3 + 1}

Add the numbers

88 y^{4}

45 y - 88 y^{4} - 23 y = 0

Subtract the terms

More Steps

Simplify

45 y - 88 y^{4} - 23 y

Subtract the terms

More Steps

Evaluate

45 y - 23 y

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

(45 - 23) y

Subtract the numbers

22 y

22 y - 88 y^{4}

22 y - 88 y^{4} = 0

Factor the expression

22 y (1 - 4 y^{3}) = 0

Divide both sides

y (1 - 4 y^{3}) = 0

Separate the equation into 2 possible cases

y = 0 1 - 4 y^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 4 y^{3} = 0

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

- 4 y^{3} = 0 - 1

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

- 4 y^{3} = - 1

Change the signs on both sides of the equation

4 y^{3} = 1

Divide both sides

\frac{4 y ^{3}}{4} = \frac{1}{4}

Divide the numbers

y^{3} = \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 \frac{1}{4}

Calculate

y = 3 \frac{1}{4}

Simplify the root

More Steps

Evaluate

3 \frac{1}{4}

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

\frac{3 1}{3 4}

Simplify the radical expression

\frac{1}{3 4}

Multiply by the Conjugate

\frac{3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 2}{2 ^{2}}

Reduce the fraction

\frac{3 2}{2}

y = \frac{3 2}{2}

y = 0 y = \frac{3 2}{2}

Solution

y_{1} = 0, y_{2} = \frac{3 2}{2}

Alternative Form

y_{1} = 0, y_{2} \approx 0.629961

Show Solution