Write in Standard Form (3a^2-1)(-3a^2+5)

$(3 a^{2} - 1) (- 3 a^{2} + 5)$

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

Expand $(3 a^{2} - 1) (- 3 a^{2} + 5)$ using the FOIL Method.

Apply the distributive property.

$3 a^{2} (- 3 a^{2} + 5) - 1 (- 3 a^{2} + 5)$

Apply the distributive property.

$3 a^{2} (- 3 a^{2}) + 3 a^{2} \cdot 5 - 1 (- 3 a^{2} + 5)$

Apply the distributive property.

$3 a^{2} (- 3 a^{2}) + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot - 3 a^{2} a^{2} + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

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

Move $a^{2}$ .

$3 \cdot - 3 (a^{2} a^{2}) + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

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

$3 \cdot - 3 a^{2 + 2} + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

Add $2$ and $2$ .

$3 \cdot - 3 a^{4} + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

Multiply $3$ by $- 3$ .

$- 9 a^{4} + 3 a^{2} \cdot 5 - 1 (- 3 a^{2}) - 1 \cdot 5$

Multiply $5$ by $3$ .

$- 9 a^{4} + 15 a^{2} - 1 (- 3 a^{2}) - 1 \cdot 5$

Multiply $- 3$ by $- 1$ .

$- 9 a^{4} + 15 a^{2} + 3 a^{2} - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$- 9 a^{4} + 15 a^{2} + 3 a^{2} - 5$

Add $15 a^{2}$ and $3 a^{2}$ .

$- 9 a^{4} + 18 a^{2} - 5$