Simplify (5x+4)^2

${(5 x + 4)}^{2}$

Step 1

Rewrite ${(5 x + 4)}^{2}$ as $(5 x + 4) (5 x + 4)$ .

$(5 x + 4) (5 x + 4)$

Step 2

Expand $(5 x + 4) (5 x + 4)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x + 4) + 4 (5 x + 4)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 4 + 4 (5 x + 4)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 4 + 4 (5 x) + 4 \cdot 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot 4 + 4 (5 x) + 4 \cdot 4$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot 4 + 4 (5 x) + 4 \cdot 4$

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot 4 + 4 (5 x) + 4 \cdot 4$

Multiply $4$ by $5$ .

$25 x^{2} + 20 x + 4 (5 x) + 4 \cdot 4$

Multiply $5$ by $4$ .

$25 x^{2} + 20 x + 20 x + 4 \cdot 4$

Multiply $4$ by $4$ .

$25 x^{2} + 20 x + 20 x + 16$

Add $20 x$ and $20 x$ .

$25 x^{2} + 40 x + 16$