Simplify (10u-8v)(u+v)

$(10 u - 8 v) (u + v)$

Step 1

Expand $(10 u - 8 v) (u + v)$ using the FOIL Method.

Apply the distributive property.

$10 u (u + v) - 8 v (u + v)$

Apply the distributive property.

$10 u \cdot u + 10 u v - 8 v (u + v)$

Apply the distributive property.

$10 u \cdot u + 10 u v - 8 v u - 8 v \cdot v$

$10 u \cdot u + 10 u v - 8 v u - 8 v \cdot v$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $u$ by $u$ by adding the exponents.

Move $u$ .

$10 (u \cdot u) + 10 u v - 8 v u - 8 v \cdot v$

Multiply $u$ by $u$ .

$10 u^{2} + 10 u v - 8 v u - 8 v \cdot v$

$10 u^{2} + 10 u v - 8 v u - 8 v \cdot v$

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$10 u^{2} + 10 u v - 8 v u - 8 (v \cdot v)$

Multiply $v$ by $v$ .

$10 u^{2} + 10 u v - 8 v u - 8 v^{2}$

$10 u^{2} + 10 u v - 8 v u - 8 v^{2}$

$10 u^{2} + 10 u v - 8 v u - 8 v^{2}$

Subtract $8 v u$ from $10 u v$ .

Move $v$ .

$10 u^{2} + 10 u v - 8 u v - 8 v^{2}$

Subtract $8 u v$ from $10 u v$ .

$10 u^{2} + 2 u v - 8 v^{2}$

$10 u^{2} + 2 u v - 8 v^{2}$

$10 u^{2} + 2 u v - 8 v^{2}$

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