Basic Math Examples

${(2 p + 1)}^{2} - {(p - 3)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 p + 1$ and $b = p - 3$ .

$(2 p + 1 + p - 3) (2 p + 1 - (p - 3))$

Step 2

Simplify.

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Step 2.1

Add $2 p$ and $p$ .

$(3 p + 1 - 3) (2 p + 1 - (p - 3))$

Step 2.2

Subtract $3$ from $1$ .

$(3 p - 2) (2 p + 1 - (p - 3))$

Step 2.3

Apply the distributive property.

$(3 p - 2) (2 p + 1 - p - - 3)$

Step 2.4

Multiply $- 1$ by $- 3$ .

$(3 p - 2) (2 p + 1 - p + 3)$

Step 2.5

Subtract $p$ from $2 p$ .

$(3 p - 2) (p + 1 + 3)$

Step 2.6

Add $1$ and $3$ .

$(3 p - 2) (p + 4)$