Solve (3x^5 5x^3 7x)-x(x 1)(x^2)(x-1)(x-2)

Question

Simplify the expression

105 x^{9} - x^{6} + 3 x^{5} - 2 x^{4}

Evaluate

(3 x^{5} \times 5 x^{3} \times 7 x) - x (x \times 1) x^{2} (x - 1) (x - 2)

Remove the parentheses

(3 x^{5} \times 5 x^{3} \times 7 x) - x \times x \times 1 \times x^{2} (x - 1) (x - 2)

Multiply

More Steps

Multiply the terms

3 x^{5} \times 5 x^{3} \times 7 x

Multiply the terms

More Steps

Evaluate

3 \times 5 \times 7

Multiply the terms

15 \times 7

Multiply the numbers

105

105 x^{5} \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

105 x^{5 + 3 + 1}

Add the numbers

105 x^{9}

105 x^{9} - x \times x \times 1 \times x^{2} (x - 1) (x - 2)

Multiply the terms

More Steps

Multiply the terms

x \times x \times 1 \times x^{2} (x - 1) (x - 2)

Rewrite the expression

x \times x \times x^{2} (x - 1) (x - 2)

Multiply the terms with the same base by adding their exponents

x^{1 + 2} \times x (x - 1) (x - 2)

Add the numbers

x^{3} \times x (x - 1) (x - 2)

Multiply the terms with the same base by adding their exponents

x^{1 + 3} (x - 1) (x - 2)

Add the numbers

x^{4} (x - 1) (x - 2)

105 x^{9} - x^{4} (x - 1) (x - 2)

Solution

More Steps

Calculate

- x^{4} (x - 1) (x - 2)

Simplify

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Evaluate

- x^{4} (x - 1)

Apply the distributive property

- x^{4} \times x - (- x^{4} \times 1)

Multiply the terms

- x^{5} - (- x^{4} \times 1)

Any expression multiplied by 1 remains the same

- x^{5} - (- x^{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

- x^{5} + x^{4}

(- x^{5} + x^{4}) (x - 2)

Apply the distributive property

- x^{5} \times x - (- x^{5} \times 2) + x^{4} \times x - x^{4} \times 2

Multiply the terms

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Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

- x^{6} - (- x^{5} \times 2) + x^{4} \times x - x^{4} \times 2

Use the commutative property to reorder the terms

- x^{6} - (- 2 x^{5}) + x^{4} \times x - x^{4} \times 2

Multiply the terms

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Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

- x^{6} - (- 2 x^{5}) + x^{5} - x^{4} \times 2

Use the commutative property to reorder the terms

- x^{6} - (- 2 x^{5}) + x^{5} - 2 x^{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

- x^{6} + 2 x^{5} + x^{5} - 2 x^{4}

Add the terms

More Steps

Evaluate

2 x^{5} + x^{5}

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

(2 + 1) x^{5}

Add the numbers

3 x^{5}

- x^{6} + 3 x^{5} - 2 x^{4}

105 x^{9} - x^{6} + 3 x^{5} - 2 x^{4}

Show Solution

Factor the expression

(105 x^{5} - x^{2} + 3 x - 2) x^{4}

Evaluate

(3 x^{5} \times 5 x^{3} \times 7 x) - x (x \times 1) x^{2} (x - 1) (x - 2)

Remove the parentheses

(3 x^{5} \times 5 x^{3} \times 7 x) - x \times x \times 1 \times x^{2} (x - 1) (x - 2)

Multiply

More Steps

Multiply the terms

3 x^{5} \times 5 x^{3} \times 7 x

Multiply the terms

More Steps

Evaluate

3 \times 5 \times 7

Multiply the terms

15 \times 7

Multiply the numbers

105

105 x^{5} \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

105 x^{5 + 3 + 1}

Add the numbers

105 x^{9}

105 x^{9} - x \times x \times 1 \times x^{2} (x - 1) (x - 2)

Any expression multiplied by 1 remains the same

105 x^{9} - x \times x \times x^{2} (x - 1) (x - 2)

Multiply

More Steps

Multiply the terms

x \times x \times x^{2} (x - 1) (x - 2)

Multiply the terms with the same base by adding their exponents

x^{1 + 2} \times x (x - 1) (x - 2)

Add the numbers

x^{3} \times x (x - 1) (x - 2)

Multiply the terms with the same base by adding their exponents

x^{1 + 3} (x - 1) (x - 2)

Add the numbers

x^{4} (x - 1) (x - 2)

105 x^{9} - x^{4} (x - 1) (x - 2)

Rewrite the expression

105 x^{5} \times x^{4} + (- x + 1) (x - 2) x^{4}

Factor out x^{4} from the expression

(105 x^{5} + (- x + 1) (x - 2)) x^{4}

Solution

(105 x^{5} - x^{2} + 3 x - 2) x^{4}

Show Solution