Algebra Examples

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

Step 1

Rewrite

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

$(x - 1) (x - 1)$ .

$4 ((x - 1) (x - 1))$

Step 2

Expand

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

Tap for more steps...

Step 2.1

Apply the distributive property.

$4 (x (x - 1) - 1 (x - 1))$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply

$x$ by

$x$ .

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

Step 3.1.2

Move

$- 1$ to the left of

$x$ .

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

Step 3.1.3

Rewrite

$- 1 x$ as

$- x$ .

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

Step 3.1.4

Rewrite

$- 1 x$ as

$- x$ .

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

Step 3.1.5

Multiply

$- 1$ by

$- 1$ .

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

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

Step 3.2

Subtract

$x$ from

$- x$ .

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

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

Tap for more steps...

Step 5.1

Multiply

$- 2$ by

$4$ .

$4 x^{2} - 8 x + 4 \cdot 1$

Step 5.2

Multiply

$4$ by

$1$ .

$4 x^{2} - 8 x + 4$

$4 x^{2} - 8 x + 4$

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

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















7

7

8

8

9

9













≤

≤





















4

4

5

5

6

6

/

/

^

^

×

×

>

>









∩

∩

∪

∪





1

1

2

2

3

3

-

-

+

+

÷

÷

<

<









π

π

∞

∞



,

,

0

0

.

.

%

%



=

=









$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$