Factor (u+2)^3+8v^3

${(u + 2)}^{3} + 8 v^{3}$

Step 1

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

${(u + 2)}^{3} + {(2 v)}^{3}$

Step 2

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

$(u + 2 + 2 v) ({(u + 2)}^{2} - (u + 2) (2 v) + {(2 v)}^{2})$

Step 3

Simplify.

Rewrite ${(u + 2)}^{2}$ as $(u + 2) (u + 2)$ .

$(u + 2 + 2 v) ((u + 2) (u + 2) - (u + 2) (2 v) + {(2 v)}^{2})$

Expand $(u + 2) (u + 2)$ using the FOIL Method.

Apply the distributive property.

$(u + 2 + 2 v) (u (u + 2) + 2 (u + 2) - (u + 2) (2 v) + {(2 v)}^{2})$

Apply the distributive property.

$(u + 2 + 2 v) (u \cdot u + u \cdot 2 + 2 (u + 2) - (u + 2) (2 v) + {(2 v)}^{2})$

Apply the distributive property.

$(u + 2 + 2 v) (u \cdot u + u \cdot 2 + 2 u + 2 \cdot 2 - (u + 2) (2 v) + {(2 v)}^{2})$

Simplify and combine like terms.

Simplify each term.

Multiply $u$ by $u$ .

$(u + 2 + 2 v) (u^{2} + u \cdot 2 + 2 u + 2 \cdot 2 - (u + 2) (2 v) + {(2 v)}^{2})$

Move $2$ to the left of $u$ .

$(u + 2 + 2 v) (u^{2} + 2 u + 2 u + 2 \cdot 2 - (u + 2) (2 v) + {(2 v)}^{2})$

Multiply $2$ by $2$ .

$(u + 2 + 2 v) (u^{2} + 2 u + 2 u + 4 - (u + 2) (2 v) + {(2 v)}^{2})$

Add $2 u$ and $2 u$ .

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - (u + 2) (2 v) + {(2 v)}^{2})$

Apply the distributive property.

$(u + 2 + 2 v) (u^{2} + 4 u + 4 + (- u - 1 \cdot 2) (2 v) + {(2 v)}^{2})$

Multiply $- 1$ by $2$ .

$(u + 2 + 2 v) (u^{2} + 4 u + 4 + (- u - 2) (2 v) + {(2 v)}^{2})$

Apply the distributive property.

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - u (2 v) - 2 (2 v) + {(2 v)}^{2})$

Rewrite using the commutative property of multiplication.

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - 1 \cdot 2 u v - 2 (2 v) + {(2 v)}^{2})$

Multiply $2$ by $- 2$ .

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - 1 \cdot 2 u v - 4 v + {(2 v)}^{2})$

Multiply $- 1$ by $2$ .

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - 2 u v - 4 v + {(2 v)}^{2})$

Apply the product rule to $2 v$ .

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - 2 u v - 4 v + 2^{2} v^{2})$

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

$(u + 2 + 2 v) (u^{2} + 4 u + 4 - 2 u v - 4 v + 4 v^{2})$

Factor (u+2)^3+8v^3

Related Questions

Support LCMGCF.com by disabling your adblocker.