Algebra Examples

${(x - 4)}^{2} - {(10 x + 1)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x - 4$ and $b = 10 x + 1$ .

$(x - 4 + 10 x + 1) (x - 4 - (10 x + 1))$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Add $x$ and $10 x$ .

$(11 x - 4 + 1) (x - 4 - (10 x + 1))$

Step 2.2

Add $- 4$ and $1$ .

$(11 x - 3) (x - 4 - (10 x + 1))$

Step 2.3

Apply the distributive property.

$(11 x - 3) (x - 4 - (10 x) - 1 \cdot 1)$

Step 2.4

Multiply $10$ by $- 1$ .

$(11 x - 3) (x - 4 - 10 x - 1 \cdot 1)$

Step 2.5

Multiply $- 1$ by $1$ .

$(11 x - 3) (x - 4 - 10 x - 1)$

Step 2.6

Subtract $10 x$ from $x$ .

$(11 x - 3) (- 9 x - 4 - 1)$

Step 2.7

Subtract $1$ from $- 4$ .

$(11 x - 3) (- 9 x - 5)$

Step 3

Factor.

Tap for more steps...

Step 3.1

Factor $- 1$ out of $- 9 x - 5$ .

Tap for more steps...

Step 3.1.1

Factor $- 1$ out of $- 9 x$ .

$(11 x - 3) (- (9 x) - 5)$

Step 3.1.2

Rewrite $- 5$ as $- 1 (5)$ .

$(11 x - 3) (- (9 x) - 1 (5))$

Step 3.1.3

Factor $- 1$ out of $- (9 x) - 1 (5)$ .

$(11 x - 3) (- (9 x + 5))$

Step 3.2

Remove unnecessary parentheses.

$(11 x - 3) \cdot - 1 (9 x + 5)$

Step 4

Factor out negative.

$- ((11 x - 3) (9 x + 5))$

Step 5

Remove unnecessary parentheses.

$- (11 x - 3) (9 x + 5)$