Simplify 5(x-1)^2

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

Step 1

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

$5 ((x - 1) (x - 1))$

Step 2

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

Apply the distributive property.

$5 (x (x - 1) - 1 (x - 1))$

Apply the distributive property.

$5 (x \cdot x + x \cdot - 1 - 1 (x - 1))$

Apply the distributive property.

$5 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

$5 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

$5 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1)$

Rewrite $- 1 x$ as $- x$ .

$5 (x^{2} - x - 1 x - 1 \cdot - 1)$

Rewrite $- 1 x$ as $- x$ .

$5 (x^{2} - x - x - 1 \cdot - 1)$

Multiply $- 1$ by $- 1$ .

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

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

Subtract $x$ from $- x$ .

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

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

Multiply $- 2$ by $5$ .

$5 x^{2} - 10 x + 5 \cdot 1$

Multiply $5$ by $1$ .

$5 x^{2} - 10 x + 5$

$5 x^{2} - 10 x + 5$

Related Questions