Simplify -3a^2(5a^2-3a+5)

$- 3 a^{2} (5 a^{2} - 3 a + 5)$

Step 1

Apply the distributive property.

$- 3 a^{2} (5 a^{2}) - 3 a^{2} (- 3 a) - 3 a^{2} \cdot 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 a^{2} a^{2} - 3 a^{2} (- 3 a) - 3 a^{2} \cdot 5$

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 a^{2} a^{2} - 3 \cdot - 3 a^{2} a - 3 a^{2} \cdot 5$

Multiply $5$ by $- 3$ .

$- 3 \cdot 5 a^{2} a^{2} - 3 \cdot - 3 a^{2} a - 15 a^{2}$

Step 3

Simplify each term.

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

Move $a^{2}$ .

$- 3 \cdot 5 (a^{2} a^{2}) - 3 \cdot - 3 a^{2} a - 15 a^{2}$

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

$- 3 \cdot 5 a^{2 + 2} - 3 \cdot - 3 a^{2} a - 15 a^{2}$

Add $2$ and $2$ .

$- 3 \cdot 5 a^{4} - 3 \cdot - 3 a^{2} a - 15 a^{2}$

Multiply $- 3$ by $5$ .

$- 15 a^{4} - 3 \cdot - 3 a^{2} a - 15 a^{2}$

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

Move $a$ .

$- 15 a^{4} - 3 \cdot - 3 (a \cdot a^{2}) - 15 a^{2}$

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

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

$- 15 a^{4} - 3 \cdot - 3 (a^{1} a^{2}) - 15 a^{2}$

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

$- 15 a^{4} - 3 \cdot - 3 a^{1 + 2} - 15 a^{2}$

Add $1$ and $2$ .

$- 15 a^{4} - 3 \cdot - 3 a^{3} - 15 a^{2}$

Multiply $- 3$ by $- 3$ .

$- 15 a^{4} + 9 a^{3} - 15 a^{2}$