Algebra Examples

${(5 x + 6)}^{2} - {(2 x + 1)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x + 6$ and $b = 2 x + 1$ .

$(5 x + 6 + 2 x + 1) (5 x + 6 - (2 x + 1))$

Step 2

Simplify.

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Step 2.1

Add $5 x$ and $2 x$ .

$(7 x + 6 + 1) (5 x + 6 - (2 x + 1))$

Step 2.2

Add $6$ and $1$ .

$(7 x + 7) (5 x + 6 - (2 x + 1))$

Step 2.3

Factor $7$ out of $7 x + 7$ .

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Step 2.3.1

Factor $7$ out of $7 x$ .

$(7 (x) + 7) (5 x + 6 - (2 x + 1))$

Step 2.3.2

Factor $7$ out of $7$ .

$(7 (x) + 7 (1)) (5 x + 6 - (2 x + 1))$

Step 2.3.3

Factor $7$ out of $7 (x) + 7 (1)$ .

$7 (x + 1) (5 x + 6 - (2 x + 1))$

Step 2.4

Apply the distributive property.

$7 (x + 1) (5 x + 6 - (2 x) - 1 \cdot 1)$

Step 2.5

Multiply $2$ by $- 1$ .

$7 (x + 1) (5 x + 6 - 2 x - 1 \cdot 1)$

Step 2.6

Multiply $- 1$ by $1$ .

$7 (x + 1) (5 x + 6 - 2 x - 1)$

Step 2.7

Subtract $2 x$ from $5 x$ .

$7 (x + 1) (3 x + 6 - 1)$

Step 2.8

Subtract $1$ from $6$ .

$7 (x + 1) (3 x + 5)$