Write in Standard Form 2(4x+2)^2=2x+1

$2 {(4 x + 2)}^{2} = 2 x + 1$

Move all the expressions to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$2 {(4 x + 2)}^{2} - 2 x = 1$

Subtract $1$ from both sides of the equation.

$2 {(4 x + 2)}^{2} - 2 x - 1 = 0$

Simplify $2 {(4 x + 2)}^{2} - 2 x - 1$ .

Simplify each term.

Rewrite ${(4 x + 2)}^{2}$ as $(4 x + 2) (4 x + 2)$ .

$2 ((4 x + 2) (4 x + 2)) - 2 x - 1 = 0$

Expand $(4 x + 2) (4 x + 2)$ using the FOIL Method.

Apply the distributive property.

$2 (4 x (4 x + 2) + 2 (4 x + 2)) - 2 x - 1 = 0$

Apply the distributive property.

$2 (4 x (4 x) + 4 x \cdot 2 + 2 (4 x + 2)) - 2 x - 1 = 0$

Apply the distributive property.

$2 (4 x (4 x) + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 (4 \cdot 4 x \cdot x + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

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

Move $x$ .

$2 (4 \cdot 4 (x \cdot x) + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

Multiply $x$ by $x$ .

$2 (4 \cdot 4 x^{2} + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

Multiply $4$ by $4$ .

$2 (16 x^{2} + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

Multiply $2$ by $4$ .

$2 (16 x^{2} + 8 x + 2 (4 x) + 2 \cdot 2) - 2 x - 1 = 0$

Multiply $4$ by $2$ .

$2 (16 x^{2} + 8 x + 8 x + 2 \cdot 2) - 2 x - 1 = 0$

Multiply $2$ by $2$ .

$2 (16 x^{2} + 8 x + 8 x + 4) - 2 x - 1 = 0$

Add $8 x$ and $8 x$ .

$2 (16 x^{2} + 16 x + 4) - 2 x - 1 = 0$

Apply the distributive property.

$2 (16 x^{2}) + 2 (16 x) + 2 \cdot 4 - 2 x - 1 = 0$

Simplify.

Multiply $16$ by $2$ .

$32 x^{2} + 2 (16 x) + 2 \cdot 4 - 2 x - 1 = 0$

Multiply $16$ by $2$ .

$32 x^{2} + 32 x + 2 \cdot 4 - 2 x - 1 = 0$

Multiply $2$ by $4$ .

$32 x^{2} + 32 x + 8 - 2 x - 1 = 0$

Subtract $2 x$ from $32 x$ .

$32 x^{2} + 30 x + 8 - 1 = 0$

Subtract $1$ from $8$ .

$32 x^{2} + 30 x + 7 = 0$

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

$a x^{2} + b x + c = 0$

The standard form is $32 x^{2} + 30 x + 7$ .

$32 x^{2} + 30 x + 7 = 0$

Write in Standard Form 2(4x+2)^2=2x+1

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