Simplify 0.5x^2(0.5x+2)

$0.5 x^{2} (0.5 x + 2)$

Step 1

Apply the distributive property.

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

Step 2

Rewrite using the commutative property of multiplication.

$0.5 \cdot 0.5 x^{2} x + 0.5 x^{2} \cdot 2$

Step 3

Multiply $0.5 x^{2} \cdot 2$ .

Multiply $2$ by $0.5$ .

$0.5 \cdot 0.5 x^{2} x + 1 x^{2}$

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

$0.5 \cdot 0.5 x^{2} x + x^{2}$

Step 4

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

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

Raise $x$ to the power of $1$ .

$0.5 \cdot 0.5 (x^{1} x^{2}) + x^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$0.5 \cdot 0.5 x^{1 + 2} + x^{2}$

Add $1$ and $2$ .

$0.5 \cdot 0.5 x^{3} + x^{2}$

Multiply $0.5$ by $0.5$ .

$0.25 x^{3} + x^{2}$