Precalculus Examples

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

Step 1

Rewrite $4$ as $2^{2}$ .

$2^{2} - {(x - 1)}^{2}$

Step 2

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

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Subtract $1$ from $2$ .

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $- 1$ by $- 1$ .

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

Step 3.4

Add $2$ and $1$ .

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

Step 4

Factor.

Tap for more steps...

Step 4.1

Factor $- 1$ out of $- x + 3$ .

Tap for more steps...

Step 4.1.1

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

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

Step 4.1.2

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 4.1.3

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

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

Step 4.2

Remove unnecessary parentheses.

$(x + 1) \cdot - 1 (x - 3)$

Step 5

Factor out negative.

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

Step 6

Remove unnecessary parentheses.

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