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

Question

Simplify the expression

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

Evaluate

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

Remove the parentheses

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

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

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

Solution

More Steps

Calculate

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

Simplify

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the terms

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

Any expression multiplied by 1 remains the same

- 2 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

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

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

Apply the distributive property

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

Multiply the terms

More Steps

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}

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

Multiply the numbers

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

Multiply the terms

More Steps

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}

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

Multiply the numbers

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

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

Add the terms

More Steps

Evaluate

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

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

(4 + 2) x^{5}

Add the numbers

6 x^{5}

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

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

Show Solution

Factor the expression

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

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

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

Rewrite the expression

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

Factor out x^{4} from the expression

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

Solution

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

Show Solution