Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite ${(1 - x)}^{2}$ as $(1 - x) (1 - x)$ .

$y = (1 - x) (1 - x) - 4$

Step 1.1.2

Expand $(1 - x) (1 - x)$ using the FOIL Method.

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$y = 1 (1 - x) - x (1 - x) - 4$

Step 1.1.2.2

Apply the distributive property.

$y = 1 \cdot 1 + 1 (- x) - x (1 - x) - 4$

Step 1.1.2.3

Apply the distributive property.

$y = 1 \cdot 1 + 1 (- x) - x \cdot 1 - x (- x) - 4$

Step 1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Multiply $1$ by $1$ .

$y = 1 + 1 (- x) - x \cdot 1 - x (- x) - 4$

Step 1.1.3.1.2

Multiply $- x$ by $1$ .

$y = 1 - x - x \cdot 1 - x (- x) - 4$

Step 1.1.3.1.3

Multiply $- 1$ by $1$ .

$y = 1 - x - x - x (- x) - 4$

Step 1.1.3.1.4

Rewrite using the commutative property of multiplication.

$y = 1 - x - x - 1 \cdot - 1 x \cdot x - 4$

Step 1.1.3.1.5

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.5.1

Move $x$ .

$y = 1 - x - x - 1 \cdot - 1 (x \cdot x) - 4$

Step 1.1.3.1.5.2

Multiply $x$ by $x$ .

$y = 1 - x - x - 1 \cdot - 1 x^{2} - 4$

Step 1.1.3.1.6

Multiply $- 1$ by $- 1$ .

$y = 1 - x - x + 1 x^{2} - 4$

Step 1.1.3.1.7

Multiply $x^{2}$ by $1$ .

$y = 1 - x - x + x^{2} - 4$

Step 1.1.3.2

Subtract $x$ from $- x$ .

$y = 1 - 2 x + x^{2} - 4$

Step 1.2

Simplify the expression.

Tap for more steps...

Step 1.2.1

Subtract $4$ from $1$ .

$y = - 2 x + x^{2} - 3$

Step 1.2.2

Reorder $- 2 x$ and $x^{2}$ .

$y = x^{2} - 2 x - 3$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(1, \infty)$

Decreasing on: $(- \infty, 1)$

Step 3