Algebra Examples

$y + 1 = {(3^{x + 1})}^{2}$

Step 1

Solve for $y$ .

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Step 1.1

Multiply the exponents in ${(3^{x + 1})}^{2}$ .

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Step 1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y + 1 = 3^{(x + 1) \cdot 2}$

Step 1.1.2

Apply the distributive property.

$y + 1 = 3^{x \cdot 2 + 1 \cdot 2}$

Step 1.1.3

Move $2$ to the left of $x$ .

$y + 1 = 3^{2 \cdot x + 1 \cdot 2}$

Step 1.1.4

Multiply $2$ by $1$ .

$y + 1 = 3^{2 x + 2}$

Step 1.2

Subtract $1$ from both sides of the equation.

$y = 3^{2 x + 2} - 1$

Step 2

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

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

Step 3

The standard form is $3^{2 x + 2} - 1$ .

$y = 3^{2 x + 2} - 1$

Step 4