Algebra Examples

${(9 n - \frac{4}{7} z)}^{2}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $z$ and $\frac{4}{7}$ .

${(9 n - \frac{z \cdot 4}{7})}^{2}$

Step 1.1.2

Move $4$ to the left of $z$ .

${(9 n - \frac{4 z}{7})}^{2}$

Step 1.2

Rewrite ${(9 n - \frac{4 z}{7})}^{2}$ as $(9 n - \frac{4 z}{7}) (9 n - \frac{4 z}{7})$ .

$(9 n - \frac{4 z}{7}) (9 n - \frac{4 z}{7})$

Step 2

Expand $(9 n - \frac{4 z}{7}) (9 n - \frac{4 z}{7})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$9 n (9 n - \frac{4 z}{7}) - \frac{4 z}{7} (9 n - \frac{4 z}{7})$

Step 2.2

Apply the distributive property.

$9 n (9 n) + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n - \frac{4 z}{7})$

Step 2.3

Apply the distributive property.

$9 n (9 n) + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

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.

$9 \cdot 9 n \cdot n + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.2

Multiply $n$ by $n$ by adding the exponents.

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Step 3.1.2.1

Move $n$ .

$9 \cdot 9 (n \cdot n) + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.2.2

Multiply $n$ by $n$ .

$9 \cdot 9 n^{2} + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.3

Multiply $9$ by $9$ .

$81 n^{2} + 9 n (- \frac{4 z}{7}) - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.4

Multiply $9 n (- \frac{4 z}{7})$ .

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Step 3.1.4.1

Multiply $- 1$ by $9$ .

$81 n^{2} - 9 n \frac{4 z}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.4.2

Combine $- 9$ and $\frac{4 z}{7}$ .

$81 n^{2} + n \frac{- 9 (4 z)}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.4.3

Multiply $4$ by $- 9$ .

$81 n^{2} + n \frac{- 36 z}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.4.4

Combine $n$ and $\frac{- 36 z}{7}$ .

$81 n^{2} + \frac{n (- 36 z)}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.5

Remove unnecessary parentheses.

$81 n^{2} + \frac{n \cdot - 36 z}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.6

Move $- 36$ to the left of $n$ .

$81 n^{2} + \frac{- 36 \cdot n z}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.7

Move the negative in front of the fraction.

$81 n^{2} - \frac{36 \cdot n z}{7} - \frac{4 z}{7} (9 n) - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.8

Multiply $- \frac{4 z}{7} (9 n)$ .

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Step 3.1.8.1

Multiply $9$ by $- 1$ .

$81 n^{2} - \frac{36 n z}{7} - 9 \frac{4 z}{7} n - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.8.2

Combine $- 9$ and $\frac{4 z}{7}$ .

$81 n^{2} - \frac{36 n z}{7} + \frac{- 9 (4 z)}{7} n - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.8.3

Multiply $4$ by $- 9$ .

$81 n^{2} - \frac{36 n z}{7} + \frac{- 36 z}{7} n - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.8.4

Combine $\frac{- 36 z}{7}$ and $n$ .

$81 n^{2} - \frac{36 n z}{7} + \frac{- 36 z n}{7} - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.9

Move the negative in front of the fraction.

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} - \frac{4 z}{7} (- \frac{4 z}{7})$

Step 3.1.10

Multiply $- \frac{4 z}{7} (- \frac{4 z}{7})$ .

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Step 3.1.10.1

Multiply $- 1$ by $- 1$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + 1 \frac{4 z}{7} \frac{4 z}{7}$

Step 3.1.10.2

Multiply $\frac{4 z}{7}$ by $1$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{4 z}{7} \cdot \frac{4 z}{7}$

Step 3.1.10.3

Multiply $\frac{4 z}{7}$ by $\frac{4 z}{7}$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{4 z (4 z)}{7 \cdot 7}$

Step 3.1.10.4

Multiply $4$ by $4$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 z \cdot z}{7 \cdot 7}$

Step 3.1.10.5

Raise $z$ to the power of $1$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 (z^{1} z)}{7 \cdot 7}$

Step 3.1.10.6

Raise $z$ to the power of $1$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 (z^{1} z^{1})}{7 \cdot 7}$

Step 3.1.10.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 z^{1 + 1}}{7 \cdot 7}$

Step 3.1.10.8

Add $1$ and $1$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 z^{2}}{7 \cdot 7}$

Step 3.1.10.9

Multiply $7$ by $7$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 z n}{7} + \frac{16 z^{2}}{49}$

Step 3.2

Subtract $\frac{36 z n}{7}$ from $- \frac{36 n z}{7}$ .

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Step 3.2.1

Move $z$ .

$81 n^{2} - \frac{36 n z}{7} - \frac{36 n z}{7} + \frac{16 z^{2}}{49}$

Step 3.2.2

Subtract $\frac{36 n z}{7}$ from $- \frac{36 n z}{7}$ .

$81 n^{2} - 2 \frac{36 n z}{7} + \frac{16 z^{2}}{49}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2 \frac{36 n z}{7}$ .

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Step 4.1.1

Combine $- 2$ and $\frac{36 n z}{7}$ .

$81 n^{2} + \frac{- 2 (36 n z)}{7} + \frac{16 z^{2}}{49}$

Step 4.1.2

Multiply $36$ by $- 2$ .

$81 n^{2} + \frac{- 72 (n z)}{7} + \frac{16 z^{2}}{49}$

Step 4.2

Move the negative in front of the fraction.

$81 n^{2} - \frac{72 n z}{7} + \frac{16 z^{2}}{49}$