Basic Math Examples

$(4 r - \frac{1}{7}) (4 r + \frac{1}{7})$

Step 1

Expand $(4 r - \frac{1}{7}) (4 r + \frac{1}{7})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 r (4 r + \frac{1}{7}) - \frac{1}{7} (4 r + \frac{1}{7})$

Step 1.2

Apply the distributive property.

$4 r (4 r) + 4 r \frac{1}{7} - \frac{1}{7} (4 r + \frac{1}{7})$

Step 1.3

Apply the distributive property.

$4 r (4 r) + 4 r \frac{1}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

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.

$4 \cdot 4 r \cdot r + 4 r \frac{1}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.2

Multiply $r$ by $r$ by adding the exponents.

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Step 2.1.2.1

Move $r$ .

$4 \cdot 4 (r \cdot r) + 4 r \frac{1}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.2.2

Multiply $r$ by $r$ .

$4 \cdot 4 r^{2} + 4 r \frac{1}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.3

Multiply $4$ by $4$ .

$16 r^{2} + 4 r \frac{1}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.4

Multiply $4 r \frac{1}{7}$ .

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Step 2.1.4.1

Combine $4$ and $\frac{1}{7}$ .

$16 r^{2} + r \frac{4}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.4.2

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

$16 r^{2} + \frac{r \cdot 4}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.5

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

$16 r^{2} + \frac{4 \cdot r}{7} - \frac{1}{7} (4 r) - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.6

Multiply $- \frac{1}{7} (4 r)$ .

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Step 2.1.6.1

Multiply $4$ by $- 1$ .

$16 r^{2} + \frac{4 r}{7} - 4 (\frac{1}{7}) r - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.6.2

Combine $- 4$ and $\frac{1}{7}$ .

$16 r^{2} + \frac{4 r}{7} + \frac{- 4}{7} r - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.6.3

Combine $\frac{- 4}{7}$ and $r$ .

$16 r^{2} + \frac{4 r}{7} + \frac{- 4 r}{7} - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.7

Move the negative in front of the fraction.

$16 r^{2} + \frac{4 r}{7} - \frac{4 r}{7} - \frac{1}{7} \cdot \frac{1}{7}$

Step 2.1.8

Multiply $- \frac{1}{7} \cdot \frac{1}{7}$ .

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Step 2.1.8.1

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

$16 r^{2} + \frac{4 r}{7} - \frac{4 r}{7} - \frac{1}{7 \cdot 7}$

Step 2.1.8.2

Multiply $7$ by $7$ .

$16 r^{2} + \frac{4 r}{7} - \frac{4 r}{7} - \frac{1}{49}$

Step 2.2

Subtract $\frac{4 r}{7}$ from $\frac{4 r}{7}$ .

$16 r^{2} + 0 - \frac{1}{49}$

Step 2.3

Add $16 r^{2}$ and $0$ .

$16 r^{2} - \frac{1}{49}$