Solve (x^3)^6-(x-3)^6

Question

Simplify the expression

x^{18} - x^{6} + 18 x^{5} - 135 x^{4} + 540 x^{3} - 1215 x^{2} + 1458 x - 729

Show Solution

(x^{3} - x + 3) (x^{6} + x^{4} - 3 x^{3} + x^{2} - 6 x + 9) (x^{3} + x - 3) (x^{6} - x^{4} + 3 x^{3} + x^{2} - 6 x + 9)

Evaluate

(x^{3})^{6} - (x - 3)^{6}

Evaluate

More Steps

x^{18} - (x - 3)^{6}

Rewrite the expression in exponential form

(x^{9})^{2} - ((x - 3)^{3})^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x^{9} - (x - 3)^{3}) (x^{9} + (x - 3)^{3})

Evaluate

(x^{9} - x^{3} + 9 x^{2} - 27 x + 27) (x^{9} + (x - 3)^{3})

Evaluate

(x^{9} - x^{3} + 9 x^{2} - 27 x + 27) (x^{9} + x^{3} - 9 x^{2} + 27 x - 27)

Factor the expression

More Steps

(x^{3} - x + 3) (x^{6} + x^{4} - 3 x^{3} + x^{2} - 6 x + 9) (x^{9} + x^{3} - 9 x^{2} + 27 x - 27)

Solution

More Steps

(x^{3} - x + 3) (x^{6} + x^{4} - 3 x^{3} + x^{2} - 6 x + 9) (x^{3} + x - 3) (x^{6} - x^{4} + 3 x^{3} + x^{2} - 6 x + 9)

Show Solution