Solve (10x 8x^(5)-2) (12 x-6x^(4))-(x^(4)-x^(2))

Question

Simplify the expression

960 x^{7} - 480 x^{10} - 24 x + 11 x^{4} + x^{2}

Evaluate

(10 x \times 8 x^{5} - 2) (12 x - 6 x^{4}) - (x^{4} - x^{2})

Multiply

More Steps

Multiply the terms

10 x \times 8 x^{5}

Multiply the terms

80 x \times x^{5}

Multiply the terms with the same base by adding their exponents

80 x^{1 + 5}

Add the numbers

80 x^{6}

(80 x^{6} - 2) (12 x - 6 x^{4}) - (x^{4} - x^{2})

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

(80 x^{6} - 2) (12 x - 6 x^{4}) - x^{4} + x^{2}

Expand the expression

More Steps

Calculate

(80 x^{6} - 2) (12 x - 6 x^{4})

Apply the distributive property

80 x^{6} \times 12 x - 80 x^{6} \times 6 x^{4} - 2 \times 12 x - (- 2 \times 6 x^{4})

Multiply the terms

More Steps

Evaluate

80 x^{6} \times 12 x

Multiply the numbers

960 x^{6} \times x

Multiply the terms

960 x^{7}

960 x^{7} - 80 x^{6} \times 6 x^{4} - 2 \times 12 x - (- 2 \times 6 x^{4})

Multiply the terms

More Steps

Evaluate

80 x^{6} \times 6 x^{4}

Multiply the numbers

480 x^{6} \times x^{4}

Multiply the terms

480 x^{10}

960 x^{7} - 480 x^{10} - 2 \times 12 x - (- 2 \times 6 x^{4})

Multiply the numbers

960 x^{7} - 480 x^{10} - 24 x - (- 2 \times 6 x^{4})

Multiply the numbers

960 x^{7} - 480 x^{10} - 24 x - (- 12 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

960 x^{7} - 480 x^{10} - 24 x + 12 x^{4}

960 x^{7} - 480 x^{10} - 24 x + 12 x^{4} - x^{4} + x^{2}

Solution

More Steps

Evaluate

12 x^{4} - x^{4}

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

(12 - 1) x^{4}

Subtract the numbers

11 x^{4}

960 x^{7} - 480 x^{10} - 24 x + 11 x^{4} + x^{2}

Show Solution

Factor the expression

x (960 x^{6} - 480 x^{9} - 24 + 11 x^{3} + x)

Evaluate

(10 x \times 8 x^{5} - 2) (12 x - 6 x^{4}) - (x^{4} - x^{2})

Multiply

More Steps

Evaluate

10 x \times 8 x^{5}

Multiply the terms

80 x \times x^{5}

Multiply the terms with the same base by adding their exponents

80 x^{1 + 5}

Add the numbers

80 x^{6}

(80 x^{6} - 2) (12 x - 6 x^{4}) - (x^{4} - x^{2})

Rewrite the expression

x (480 x^{6} - 12) (2 - x^{3}) + x (- x^{3} + x)

Factor out x from the expression

x ((480 x^{6} - 12) (2 - x^{3}) - x^{3} + x)

Solution

x (960 x^{6} - 480 x^{9} - 24 + 11 x^{3} + x)

Show Solution