Basic Math Examples

$(7 z - u) (5 z + 5 u)$

Step 1

Expand $(7 z - u) (5 z + 5 u)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 z (5 z + 5 u) - u (5 z + 5 u)$

Step 1.2

Apply the distributive property.

$7 z (5 z) + 7 z (5 u) - u (5 z + 5 u)$

Step 1.3

Apply the distributive property.

$7 z (5 z) + 7 z (5 u) - u (5 z) - u (5 u)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$7 \cdot 5 z \cdot z + 7 z (5 u) - u (5 z) - u (5 u)$

Step 2.1.2

Multiply $z$ by $z$ by adding the exponents.

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Step 2.1.2.1

Move $z$ .

$7 \cdot 5 (z \cdot z) + 7 z (5 u) - u (5 z) - u (5 u)$

Step 2.1.2.2

Multiply $z$ by $z$ .

$7 \cdot 5 z^{2} + 7 z (5 u) - u (5 z) - u (5 u)$

Step 2.1.3

Multiply $7$ by $5$ .

$35 z^{2} + 7 z (5 u) - u (5 z) - u (5 u)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$35 z^{2} + 7 \cdot 5 z u - u (5 z) - u (5 u)$

Step 2.1.5

Multiply $7$ by $5$ .

$35 z^{2} + 35 z u - u (5 z) - u (5 u)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$35 z^{2} + 35 z u - 1 \cdot 5 u z - u (5 u)$

Step 2.1.7

Multiply $- 1$ by $5$ .

$35 z^{2} + 35 z u - 5 u z - u (5 u)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$35 z^{2} + 35 z u - 5 u z - 1 \cdot 5 u \cdot u$

Step 2.1.9

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

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Step 2.1.9.1

Move $u$ .

$35 z^{2} + 35 z u - 5 u z - 1 \cdot 5 (u \cdot u)$

Step 2.1.9.2

Multiply $u$ by $u$ .

$35 z^{2} + 35 z u - 5 u z - 1 \cdot 5 u^{2}$

Step 2.1.10

Multiply $- 1$ by $5$ .

$35 z^{2} + 35 z u - 5 u z - 5 u^{2}$

Step 2.2

Subtract $5 u z$ from $35 z u$ .

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Step 2.2.1

Move $z$ .

$35 z^{2} + 35 u z - 5 u z - 5 u^{2}$

Step 2.2.2

Subtract $5 u z$ from $35 u z$ .

$35 z^{2} + 30 u z - 5 u^{2}$

Step 3

Move $35 z^{2}$ .

$30 u z - 5 u^{2} + 35 z^{2}$

Step 4

Reorder $30 u z$ and $- 5 u^{2}$ .

$- 5 u^{2} + 30 u z + 35 z^{2}$