Solve (h-5)2 (3-h)(h^3)

Question

Simplify the expression

16 h^{4} - 2 h^{5} - 30 h^{3}

Evaluate

(h - 5) \times 2 (3 - h) h^{3}

Multiply the terms

(h - 5) \times 2 h^{3} (3 - h)

Multiply the first two terms

2 h^{3} (h - 5) (3 - h)

Multiply the terms

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Evaluate

2 h^{3} (h - 5)

Apply the distributive property

2 h^{3} \times h - 2 h^{3} \times 5

Multiply the terms

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Evaluate

h^{3} \times h

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

h^{3 + 1}

Add the numbers

h^{4}

2 h^{4} - 2 h^{3} \times 5

Multiply the numbers

2 h^{4} - 10 h^{3}

(2 h^{4} - 10 h^{3}) (3 - h)

Apply the distributive property

2 h^{4} \times 3 - 2 h^{4} \times h - 10 h^{3} \times 3 - (- 10 h^{3} \times h)

Multiply the numbers

6 h^{4} - 2 h^{4} \times h - 10 h^{3} \times 3 - (- 10 h^{3} \times h)

Multiply the terms

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Evaluate

h^{4} \times h

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

h^{4 + 1}

Add the numbers

h^{5}

6 h^{4} - 2 h^{5} - 10 h^{3} \times 3 - (- 10 h^{3} \times h)

Multiply the numbers

6 h^{4} - 2 h^{5} - 30 h^{3} - (- 10 h^{3} \times h)

Multiply the terms

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Evaluate

h^{3} \times h

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

h^{3 + 1}

Add the numbers

h^{4}

6 h^{4} - 2 h^{5} - 30 h^{3} - (- 10 h^{4})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 h^{4} - 2 h^{5} - 30 h^{3} + 10 h^{4}

Solution

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Evaluate

6 h^{4} + 10 h^{4}

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

(6 + 10) h^{4}

Add the numbers

16 h^{4}

16 h^{4} - 2 h^{5} - 30 h^{3}

Show Solution

Find the roots

h_{1} = 0, h_{2} = 3, h_{3} = 5

Evaluate

(h - 5) \times 2 (3 - h) (h^{3})

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

(h - 5) \times 2 (3 - h) (h^{3}) = 0

Calculate

(h - 5) \times 2 (3 - h) h^{3} = 0

Multiply the terms

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Multiply the terms

(h - 5) \times 2 (3 - h) h^{3}

Multiply the terms

(h - 5) \times 2 h^{3} (3 - h)

Multiply the first two terms

2 h^{3} (h - 5) (3 - h)

2 h^{3} (h - 5) (3 - h) = 0

Elimination the left coefficient

h^{3} (h - 5) (3 - h) = 0

Separate the equation into 3 possible cases

h^{3} = 0 h - 5 = 0 3 - h = 0

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

h = 0 h - 5 = 0 3 - h = 0

Solve the equation

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Evaluate

h - 5 = 0

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

h = 0 + 5

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

h = 5

h = 0 h = 5 3 - h = 0

Solve the equation

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Evaluate

3 - h = 0

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

- h = 0 - 3

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

- h = - 3

Change the signs on both sides of the equation

h = 3

h = 0 h = 5 h = 3

Solution

h_{1} = 0, h_{2} = 3, h_{3} = 5

Show Solution