Basic Math Examples

${((p + r) - 1)}^{2}$

Step 1

Rewrite ${(p + r - 1)}^{2}$ as $(p + r - 1) (p + r - 1)$ .

$(p + r - 1) (p + r - 1)$

Step 2

Expand $(p + r - 1) (p + r - 1)$ by multiplying each term in the first expression by each term in the second expression.

$p \cdot p + p r + p \cdot - 1 + r p + r \cdot r + r \cdot - 1 - 1 p - 1 r - 1 \cdot - 1$

Step 3

Simplify each term.

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Step 3.1

Multiply $p$ by $p$ .

$p^{2} + p r + p \cdot - 1 + r p + r \cdot r + r \cdot - 1 - 1 p - 1 r - 1 \cdot - 1$

Step 3.2

Move $- 1$ to the left of $p$ .

$p^{2} + p r - 1 \cdot p + r p + r \cdot r + r \cdot - 1 - 1 p - 1 r - 1 \cdot - 1$

Step 3.3

Rewrite $- 1 p$ as $- p$ .

$p^{2} + p r - p + r p + r \cdot r + r \cdot - 1 - 1 p - 1 r - 1 \cdot - 1$

Step 3.4

Multiply $r$ by $r$ .

$p^{2} + p r - p + r p + r^{2} + r \cdot - 1 - 1 p - 1 r - 1 \cdot - 1$

Step 3.5

Move $- 1$ to the left of $r$ .

$p^{2} + p r - p + r p + r^{2} - 1 \cdot r - 1 p - 1 r - 1 \cdot - 1$

Step 3.6

Rewrite $- 1 r$ as $- r$ .

$p^{2} + p r - p + r p + r^{2} - r - 1 p - 1 r - 1 \cdot - 1$

Step 3.7

Rewrite $- 1 p$ as $- p$ .

$p^{2} + p r - p + r p + r^{2} - r - p - 1 r - 1 \cdot - 1$

Step 3.8

Rewrite $- 1 r$ as $- r$ .

$p^{2} + p r - p + r p + r^{2} - r - p - r - 1 \cdot - 1$

Step 3.9

Multiply $- 1$ by $- 1$ .

$p^{2} + p r - p + r p + r^{2} - r - p - r + 1$

Step 4

Add $p r$ and $r p$ .

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Step 4.1

Reorder $r$ and $p$ .

$p^{2} + p r + p r - p + r^{2} - r - p - r + 1$

Step 4.2

Add $p r$ and $p r$ .

$p^{2} + 2 p r - p + r^{2} - r - p - r + 1$

Step 5

Subtract $p$ from $- p$ .

$p^{2} + 2 p r - 2 p + r^{2} - r - r + 1$

Step 6

Subtract $r$ from $- r$ .

$p^{2} + 2 p r - 2 p + r^{2} - 2 r + 1$

Step 7

Move $- 2 p$ .

$p^{2} + 2 p r + r^{2} - 2 p - 2 r + 1$