Write in Standard Form 4a(5a^2-4)+9a

$4 a (5 a^{2} - 4) + 9 a$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

Apply the distributive property.

$4 a (5 a^{2}) + 4 a \cdot - 4 + 9 a$

Rewrite using the commutative property of multiplication.

$4 \cdot 5 a \cdot a^{2} + 4 a \cdot - 4 + 9 a$

Multiply $- 4$ by $4$ .

$4 \cdot 5 a \cdot a^{2} - 16 a + 9 a$

Simplify each term.

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

Move $a^{2}$ .

$4 \cdot 5 (a^{2} a) - 16 a + 9 a$

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

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

$4 \cdot 5 (a^{2} a^{1}) - 16 a + 9 a$

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

$4 \cdot 5 a^{2 + 1} - 16 a + 9 a$

Add $2$ and $1$ .

$4 \cdot 5 a^{3} - 16 a + 9 a$

Multiply $4$ by $5$ .

$20 a^{3} - 16 a + 9 a$

Step 3

Add $- 16 a$ and $9 a$ .

$20 a^{3} - 7 a$