Find the Product (4x+3)^2

${(4 x + 3)}^{2}$

Step 1

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

$(4 x + 3) (4 x + 3)$

Step 2

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

Apply the distributive property.

$4 x (4 x + 3) + 3 (4 x + 3)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 3 + 3 (4 x + 3)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3$

Multiply $3$ by $4$ .

$16 x^{2} + 12 x + 3 (4 x) + 3 \cdot 3$

Multiply $4$ by $3$ .

$16 x^{2} + 12 x + 12 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$16 x^{2} + 12 x + 12 x + 9$

Add $12 x$ and $12 x$ .

$16 x^{2} + 24 x + 9$