Simplify (2a+5)^2-5(4a+5)

${(2 a + 5)}^{2} - 5 (4 a + 5)$

Simplify each term.

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

$(2 a + 5) (2 a + 5) - 5 (4 a + 5)$

Expand $(2 a + 5) (2 a + 5)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a + 5) + 5 (2 a + 5) - 5 (4 a + 5)$

Apply the distributive property.

$2 a (2 a) + 2 a \cdot 5 + 5 (2 a + 5) - 5 (4 a + 5)$

Apply the distributive property.

$2 a (2 a) + 2 a \cdot 5 + 5 (2 a) + 5 \cdot 5 - 5 (4 a + 5)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a \cdot 5 + 5 (2 a) + 5 \cdot 5 - 5 (4 a + 5)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a \cdot 5 + 5 (2 a) + 5 \cdot 5 - 5 (4 a + 5)$

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

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

Multiply $5$ by $2$ .

$4 a^{2} + 10 a + 5 (2 a) + 5 \cdot 5 - 5 (4 a + 5)$

Multiply $2$ by $5$ .

$4 a^{2} + 10 a + 10 a + 5 \cdot 5 - 5 (4 a + 5)$

Multiply $5$ by $5$ .

$4 a^{2} + 10 a + 10 a + 25 - 5 (4 a + 5)$

Add $10 a$ and $10 a$ .

$4 a^{2} + 20 a + 25 - 5 (4 a + 5)$

Apply the distributive property.

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

Multiply $4$ by $- 5$ .

$4 a^{2} + 20 a + 25 - 20 a - 5 \cdot 5$

Multiply $- 5$ by $5$ .

$4 a^{2} + 20 a + 25 - 20 a - 25$

Combine the opposite terms in $4 a^{2} + 20 a + 25 - 20 a - 25$ .

Subtract $20 a$ from $20 a$ .

$4 a^{2} + 0 + 25 - 25$

Add $4 a^{2}$ and $0$ .

$4 a^{2} + 25 - 25$

Subtract $25$ from $25$ .

$4 a^{2} + 0$

Add $4 a^{2}$ and $0$ .

$4 a^{2}$