Simplify (5w+8u)(5w-8u)

$(5 w + 8 u) (5 w - 8 u)$

Expand $(5 w + 8 u) (5 w - 8 u)$ using the FOIL Method.

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Apply the distributive property.

$5 w (5 w - 8 u) + 8 u (5 w - 8 u)$

Apply the distributive property.

$5 w (5 w) + 5 w (- 8 u) + 8 u (5 w - 8 u)$

Apply the distributive property.

$5 w (5 w) + 5 w (- 8 u) + 8 u (5 w) + 8 u (- 8 u)$

Simplify and combine like terms.

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Simplify each term.

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Multiply $w$ by $w$ .

$5 \cdot 5 w^{2} + 5 w (- 8 u) + 8 u (5 w) + 8 u (- 8 u)$

Multiply $5$ by $5$ .

$25 w^{2} + 5 w (- 8 u) + 8 u (5 w) + 8 u (- 8 u)$

Rewrite using the commutative property of multiplication.

$25 w^{2} + 5 \cdot - 8 (w u) + 8 u (5 w) + 8 u (- 8 u)$

Multiply $5$ by $- 8$ .

$25 w^{2} - 40 (w u) + 8 u (5 w) + 8 u (- 8 u)$

Rewrite using the commutative property of multiplication.

$25 w^{2} - 40 w u + 8 \cdot 5 (u w) + 8 u (- 8 u)$

Multiply $8$ by $5$ .

$25 w^{2} - 40 w u + 40 (u w) + 8 u (- 8 u)$

Multiply $u$ by $u$ .

$25 w^{2} - 40 w u + 40 u w + 8 \cdot - 8 u^{2}$

Multiply $8$ by $- 8$ .

$25 w^{2} - 40 w u + 40 u w - 64 u^{2}$

Add $- 40 w u$ and $40 u w$ .

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Move $w$ .

$25 w^{2} - 40 u w + 40 u w - 64 u^{2}$

Add $- 40 u w$ and $40 u w$ .

$25 w^{2} + 0 - 64 u^{2}$

Add $25 w^{2}$ and $0$ .

$25 w^{2} - 64 u^{2}$

Simplify (5w+8u)(5w-8u)

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