Simplify -5a^2(4a^2-5a+4)

$- 5 a^{2} (4 a^{2} - 5 a + 4)$

Step 1

Apply the distributive property.

$- 5 a^{2} (4 a^{2}) - 5 a^{2} (- 5 a) - 5 a^{2} \cdot 4$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 5 \cdot 4 a^{2} a^{2} - 5 a^{2} (- 5 a) - 5 a^{2} \cdot 4$

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $- 5$ .

$- 5 \cdot 4 a^{2} a^{2} - 5 \cdot - 5 a^{2} a - 20 a^{2}$

Step 3

Simplify each term.

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

Move $a^{2}$ .

$- 5 \cdot 4 (a^{2} a^{2}) - 5 \cdot - 5 a^{2} a - 20 a^{2}$

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

$- 5 \cdot 4 a^{2 + 2} - 5 \cdot - 5 a^{2} a - 20 a^{2}$

Add $2$ and $2$ .

$- 5 \cdot 4 a^{4} - 5 \cdot - 5 a^{2} a - 20 a^{2}$

Multiply $- 5$ by $4$ .

$- 20 a^{4} - 5 \cdot - 5 a^{2} a - 20 a^{2}$

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

Move $a$ .

$- 20 a^{4} - 5 \cdot - 5 (a \cdot a^{2}) - 20 a^{2}$

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

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

$- 20 a^{4} - 5 \cdot - 5 (a^{1} a^{2}) - 20 a^{2}$

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

$- 20 a^{4} - 5 \cdot - 5 a^{1 + 2} - 20 a^{2}$

Add $1$ and $2$ .

$- 20 a^{4} - 5 \cdot - 5 a^{3} - 20 a^{2}$

Multiply $- 5$ by $- 5$ .

$- 20 a^{4} + 25 a^{3} - 20 a^{2}$