Solve for a (9x-4)(9x+4)=ax^2-b

$(9 x - 4) (9 x + 4) = a x^{2} - b$

Rewrite the equation as $a x^{2} - b = (9 x - 4) (9 x + 4)$ .

$a x^{2} - b = (9 x - 4) (9 x + 4)$

Simplify $(9 x - 4) (9 x + 4)$ .

Rewrite.

$a x^{2} - b = 0 + 0 + (9 x - 4) (9 x + 4)$

Simplify by adding zeros.

$a x^{2} - b = (9 x - 4) (9 x + 4)$

Expand $(9 x - 4) (9 x + 4)$ using the FOIL Method.

Apply the distributive property.

$a x^{2} - b = 9 x (9 x + 4) - 4 (9 x + 4)$

Apply the distributive property.

$a x^{2} - b = 9 x (9 x) + 9 x \cdot 4 - 4 (9 x + 4)$

Apply the distributive property.

$a x^{2} - b = 9 x (9 x) + 9 x \cdot 4 - 4 (9 x) - 4 \cdot 4$

Simplify terms.

Combine the opposite terms in $9 x (9 x) + 9 x \cdot 4 - 4 (9 x) - 4 \cdot 4$ .

Reorder the factors in the terms $9 x \cdot 4$ and $- 4 (9 x)$ .

$a x^{2} - b = 9 x (9 x) + 4 \cdot 9 x - 4 \cdot 9 x - 4 \cdot 4$

Subtract $4 \cdot 9 x$ from $4 \cdot 9 x$ .

$a x^{2} - b = 9 x (9 x) + 0 - 4 \cdot 4$

Add $9 x (9 x)$ and $0$ .

$a x^{2} - b = 9 x (9 x) - 4 \cdot 4$

Simplify each term.

Rewrite using the commutative property of multiplication.

$a x^{2} - b = 9 \cdot 9 x \cdot x - 4 \cdot 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$a x^{2} - b = 9 \cdot 9 (x \cdot x) - 4 \cdot 4$

Multiply $x$ by $x$ .

$a x^{2} - b = 9 \cdot 9 x^{2} - 4 \cdot 4$

Multiply $9$ by $9$ .

$a x^{2} - b = 81 x^{2} - 4 \cdot 4$

Multiply $- 4$ by $4$ .

$a x^{2} - b = 81 x^{2} - 16$

Add $b$ to both sides of the equation.

$a x^{2} = 81 x^{2} - 16 + b$

Divide each term in $a x^{2} = 81 x^{2} - 16 + b$ by $x^{2}$ and simplify.

Divide each term in $a x^{2} = 81 x^{2} - 16 + b$ by $x^{2}$ .

$\frac{a x^{2}}{x^{2}} = \frac{81 x^{2}}{x^{2}} + \frac{- 16}{x^{2}} + \frac{b}{x^{2}}$

Simplify the left side.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{a x^{2}}{x^{2}} = \frac{81 x^{2}}{x^{2}} + \frac{- 16}{x^{2}} + \frac{b}{x^{2}}$

Divide $a$ by $1$ .

$a = \frac{81 x^{2}}{x^{2}} + \frac{- 16}{x^{2}} + \frac{b}{x^{2}}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$a = \frac{81 x^{2}}{x^{2}} + \frac{- 16}{x^{2}} + \frac{b}{x^{2}}$

Divide $81$ by $1$ .

$a = 81 + \frac{- 16}{x^{2}} + \frac{b}{x^{2}}$

Move the negative in front of the fraction.

$a = 81 - \frac{16}{x^{2}} + \frac{b}{x^{2}}$

Solve for a (9x-4)(9x+4)=ax^2-b

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