Factor 24x^6-1029y^3

$24 x^{6} - 1029 y^{3}$

Step 1

Factor $3$ out of $24 x^{6} - 1029 y^{3}$ .

Factor $3$ out of $24 x^{6}$ .

$3 (8 x^{6}) - 1029 y^{3}$

Factor $3$ out of $- 1029 y^{3}$ .

$3 (8 x^{6}) + 3 (- 343 y^{3})$

Factor $3$ out of $3 (8 x^{6}) + 3 (- 343 y^{3})$ .

$3 (8 x^{6} - 343 y^{3})$

Step 2

Rewrite $8 x^{6}$ as ${(2 x^{2})}^{3}$ .

$3 ({(2 x^{2})}^{3} - 343 y^{3})$

Step 3

Rewrite $343 y^{3}$ as ${(7 y)}^{3}$ .

$3 ({(2 x^{2})}^{3} - {(7 y)}^{3})$

Step 4

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 2 x^{2}$ and $b = 7 y$ .

$3 ((2 x^{2} - (7 y)) ({(2 x^{2})}^{2} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Step 5

Factor.

Simplify.

Multiply $7$ by $- 1$ .

$3 ((2 x^{2} - 7 y) ({(2 x^{2})}^{2} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Apply the product rule to $2 x^{2}$ .

$3 ((2 x^{2} - 7 y) (2^{2} {(x^{2})}^{2} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Raise $2$ to the power of $2$ .

$3 ((2 x^{2} - 7 y) (4 {(x^{2})}^{2} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 ((2 x^{2} - 7 y) (4 x^{2 \cdot 2} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Multiply $2$ by $2$ .

$3 ((2 x^{2} - 7 y) (4 x^{4} + 2 x^{2} (7 y) + {(7 y)}^{2}))$

Rewrite using the commutative property of multiplication.

$3 ((2 x^{2} - 7 y) (4 x^{4} + 2 \cdot 7 x^{2} y + {(7 y)}^{2}))$

Multiply $2$ by $7$ .

$3 ((2 x^{2} - 7 y) (4 x^{4} + 14 x^{2} y + {(7 y)}^{2}))$

Apply the product rule to $7 y$ .

$3 ((2 x^{2} - 7 y) (4 x^{4} + 14 x^{2} y + 7^{2} y^{2}))$

Raise $7$ to the power of $2$ .

$3 ((2 x^{2} - 7 y) (4 x^{4} + 14 x^{2} y + 49 y^{2}))$

Remove unnecessary parentheses.

$3 (2 x^{2} - 7 y) (4 x^{4} + 14 x^{2} y + 49 y^{2})$

Factor 24x^6-1029y^3

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