Simplify (0.5x-3)(0.5x+3)

$(0.5 x - 3) (0.5 x + 3)$

Step 1

Expand $(0.5 x - 3) (0.5 x + 3)$ using the FOIL Method.

Apply the distributive property.

$0.5 x (0.5 x + 3) - 3 (0.5 x + 3)$

Apply the distributive property.

$0.5 x (0.5 x) + 0.5 x \cdot 3 - 3 (0.5 x + 3)$

Apply the distributive property.

$0.5 x (0.5 x) + 0.5 x \cdot 3 - 3 (0.5 x) - 3 \cdot 3$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$0.5 \cdot 0.5 x \cdot x + 0.5 x \cdot 3 - 3 (0.5 x) - 3 \cdot 3$

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

Move $x$ .

$0.5 \cdot 0.5 (x \cdot x) + 0.5 x \cdot 3 - 3 (0.5 x) - 3 \cdot 3$

Multiply $x$ by $x$ .

$0.5 \cdot 0.5 x^{2} + 0.5 x \cdot 3 - 3 (0.5 x) - 3 \cdot 3$

Multiply $0.5$ by $0.5$ .

$0.25 x^{2} + 0.5 x \cdot 3 - 3 (0.5 x) - 3 \cdot 3$

Multiply $3$ by $0.5$ .

$0.25 x^{2} + 1.5 x - 3 (0.5 x) - 3 \cdot 3$

Multiply $0.5$ by $- 3$ .

$0.25 x^{2} + 1.5 x - 1.5 x - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$0.25 x^{2} + 1.5 x - 1.5 x - 9$

Subtract $1.5 x$ from $1.5 x$ .

$0.25 x^{2} + 0 x - 9$

Step 3

Multiply $0$ by $x$ .

$0.25 x^{2} + 0 - 9$

Step 4

Add $0.25 x^{2}$ and $0$ .

$0.25 x^{2} - 9$