Write in Standard Form y=(3x+4)^2+5

$y = {(3 x + 4)}^{2} + 5$

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

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

Simplify each term.

Rewrite ${(3 x + 4)}^{2}$ as $(3 x + 4) (3 x + 4)$ .

$y = (3 x + 4) (3 x + 4) + 5$

Expand $(3 x + 4) (3 x + 4)$ using the FOIL Method.

Apply the distributive property.

$y = 3 x (3 x + 4) + 4 (3 x + 4) + 5$

Apply the distributive property.

$y = 3 x (3 x) + 3 x \cdot 4 + 4 (3 x + 4) + 5$

Apply the distributive property.

$y = 3 x (3 x) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 + 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 3 \cdot (3 x \cdot x) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 + 5$

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

Move $x$ .

$y = 3 \cdot (3 (x \cdot x)) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 + 5$

Multiply $x$ by $x$ .

$y = 3 \cdot (3 x^{2}) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 + 5$

Multiply $3$ by $3$ .

$y = 9 x^{2} + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 + 5$

Multiply $4$ by $3$ .

$y = 9 x^{2} + 12 x + 4 (3 x) + 4 \cdot 4 + 5$

Multiply $3$ by $4$ .

$y = 9 x^{2} + 12 x + 12 x + 4 \cdot 4 + 5$

Multiply $4$ by $4$ .

$y = 9 x^{2} + 12 x + 12 x + 16 + 5$

Add $12 x$ and $12 x$ .

$y = 9 x^{2} + 24 x + 16 + 5$

Add $16$ and $5$ .

$y = 9 x^{2} + 24 x + 21$