Find the Perfect Square Trinomial (5m+8)^2

${(5 m + 8)}^{2}$

Step 1

Rewrite ${(5 m + 8)}^{2}$ as $(5 m + 8) (5 m + 8)$ .

$(5 m + 8) (5 m + 8)$

Step 2

Expand $(5 m + 8) (5 m + 8)$ using the FOIL Method.

Apply the distributive property.

$5 m (5 m + 8) + 8 (5 m + 8)$

Apply the distributive property.

$5 m (5 m) + 5 m \cdot 8 + 8 (5 m + 8)$

Apply the distributive property.

$5 m (5 m) + 5 m \cdot 8 + 8 (5 m) + 8 \cdot 8$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 m \cdot m + 5 m \cdot 8 + 8 (5 m) + 8 \cdot 8$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$5 \cdot 5 (m \cdot m) + 5 m \cdot 8 + 8 (5 m) + 8 \cdot 8$

Multiply $m$ by $m$ .

$5 \cdot 5 m^{2} + 5 m \cdot 8 + 8 (5 m) + 8 \cdot 8$

Multiply $5$ by $5$ .

$25 m^{2} + 5 m \cdot 8 + 8 (5 m) + 8 \cdot 8$

Multiply $8$ by $5$ .

$25 m^{2} + 40 m + 8 (5 m) + 8 \cdot 8$

Multiply $5$ by $8$ .

$25 m^{2} + 40 m + 40 m + 8 \cdot 8$

Multiply $8$ by $8$ .

$25 m^{2} + 40 m + 40 m + 64$

Add $40 m$ and $40 m$ .

$25 m^{2} + 80 m + 64$