Basic Math Examples

${(5 a - 8 z)}^{2}$

Step 1

Rewrite ${(5 a - 8 z)}^{2}$ as $(5 a - 8 z) (5 a - 8 z)$ .

$(5 a - 8 z) (5 a - 8 z)$

Step 2

Expand $(5 a - 8 z) (5 a - 8 z)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 a (5 a - 8 z) - 8 z (5 a - 8 z)$

Step 2.2

Apply the distributive property.

$5 a (5 a) + 5 a (- 8 z) - 8 z (5 a - 8 z)$

Step 2.3

Apply the distributive property.

$5 a (5 a) + 5 a (- 8 z) - 8 z (5 a) - 8 z (- 8 z)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a + 5 a (- 8 z) - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1.2.1

Move $a$ .

$5 \cdot 5 (a \cdot a) + 5 a (- 8 z) - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.2.2

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} + 5 a (- 8 z) - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.3

Multiply $5$ by $5$ .

$25 a^{2} + 5 a (- 8 z) - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$25 a^{2} + 5 \cdot - 8 a z - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.5

Multiply $5$ by $- 8$ .

$25 a^{2} - 40 a z - 8 z (5 a) - 8 z (- 8 z)$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$25 a^{2} - 40 a z - 8 \cdot 5 z a - 8 z (- 8 z)$

Step 3.1.7

Multiply $- 8$ by $5$ .

$25 a^{2} - 40 a z - 40 z a - 8 z (- 8 z)$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$25 a^{2} - 40 a z - 40 z a - 8 \cdot - 8 z \cdot z$

Step 3.1.9

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

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Step 3.1.9.1

Move $z$ .

$25 a^{2} - 40 a z - 40 z a - 8 \cdot - 8 (z \cdot z)$

Step 3.1.9.2

Multiply $z$ by $z$ .

$25 a^{2} - 40 a z - 40 z a - 8 \cdot - 8 z^{2}$

Step 3.1.10

Multiply $- 8$ by $- 8$ .

$25 a^{2} - 40 a z - 40 z a + 64 z^{2}$

Step 3.2

Subtract $40 z a$ from $- 40 a z$ .

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Step 3.2.1

Move $z$ .

$25 a^{2} - 40 a z - 40 a z + 64 z^{2}$

Step 3.2.2

Subtract $40 a z$ from $- 40 a z$ .

$25 a^{2} - 80 a z + 64 z^{2}$