Find the Perfect Square Trinomial (2b+7)^2

${(2 b + 7)}^{2}$

Step 1

Rewrite ${(2 b + 7)}^{2}$ as $(2 b + 7) (2 b + 7)$ .

$(2 b + 7) (2 b + 7)$

Step 2

Expand $(2 b + 7) (2 b + 7)$ using the FOIL Method.

Apply the distributive property.

$2 b (2 b + 7) + 7 (2 b + 7)$

Apply the distributive property.

$2 b (2 b) + 2 b \cdot 7 + 7 (2 b + 7)$

Apply the distributive property.

$2 b (2 b) + 2 b \cdot 7 + 7 (2 b) + 7 \cdot 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 b \cdot b + 2 b \cdot 7 + 7 (2 b) + 7 \cdot 7$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$2 \cdot 2 (b \cdot b) + 2 b \cdot 7 + 7 (2 b) + 7 \cdot 7$

Multiply $b$ by $b$ .

$2 \cdot 2 b^{2} + 2 b \cdot 7 + 7 (2 b) + 7 \cdot 7$

Multiply $2$ by $2$ .

$4 b^{2} + 2 b \cdot 7 + 7 (2 b) + 7 \cdot 7$

Multiply $7$ by $2$ .

$4 b^{2} + 14 b + 7 (2 b) + 7 \cdot 7$

Multiply $2$ by $7$ .

$4 b^{2} + 14 b + 14 b + 7 \cdot 7$

Multiply $7$ by $7$ .

$4 b^{2} + 14 b + 14 b + 49$

Add $14 b$ and $14 b$ .

$4 b^{2} + 28 b + 49$