Solve for B (4a+5)^2=16a^2+Ba+25

${(4 a + 5)}^{2} = 16 a^{2} + B a + 25$

Rewrite the equation as $16 a^{2} + B a + 25 = {(4 a + 5)}^{2}$ .

$16 a^{2} + B a + 25 = {(4 a + 5)}^{2}$

Simplify ${(4 a + 5)}^{2}$ .

Rewrite.

$16 a^{2} + B a + 25 = 0 + 0 + {(4 a + 5)}^{2}$

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

$16 a^{2} + B a + 25 = (4 a + 5) (4 a + 5)$

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

Apply the distributive property.

$16 a^{2} + B a + 25 = 4 a (4 a + 5) + 5 (4 a + 5)$

Apply the distributive property.

$16 a^{2} + B a + 25 = 4 a (4 a) + 4 a \cdot 5 + 5 (4 a + 5)$

Apply the distributive property.

$16 a^{2} + B a + 25 = 4 a (4 a) + 4 a \cdot 5 + 5 (4 a) + 5 \cdot 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$16 a^{2} + B a + 25 = 4 \cdot 4 a \cdot a + 4 a \cdot 5 + 5 (4 a) + 5 \cdot 5$

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

Move $a$ .

$16 a^{2} + B a + 25 = 4 \cdot 4 (a \cdot a) + 4 a \cdot 5 + 5 (4 a) + 5 \cdot 5$

Multiply $a$ by $a$ .

$16 a^{2} + B a + 25 = 4 \cdot 4 a^{2} + 4 a \cdot 5 + 5 (4 a) + 5 \cdot 5$

Multiply $4$ by $4$ .

$16 a^{2} + B a + 25 = 16 a^{2} + 4 a \cdot 5 + 5 (4 a) + 5 \cdot 5$

Multiply $5$ by $4$ .

$16 a^{2} + B a + 25 = 16 a^{2} + 20 a + 5 (4 a) + 5 \cdot 5$

Multiply $4$ by $5$ .

$16 a^{2} + B a + 25 = 16 a^{2} + 20 a + 20 a + 5 \cdot 5$

Multiply $5$ by $5$ .

$16 a^{2} + B a + 25 = 16 a^{2} + 20 a + 20 a + 25$

Add $20 a$ and $20 a$ .

$16 a^{2} + B a + 25 = 16 a^{2} + 40 a + 25$

Move all terms not containing $B$ to the right side of the equation.

Subtract $16 a^{2}$ from both sides of the equation.

$B a + 25 = 16 a^{2} + 40 a + 25 - 16 a^{2}$

Subtract $25$ from both sides of the equation.

$B a = 16 a^{2} + 40 a + 25 - 16 a^{2} - 25$

Combine the opposite terms in $16 a^{2} + 40 a + 25 - 16 a^{2} - 25$ .

Subtract $16 a^{2}$ from $16 a^{2}$ .

$B a = 40 a + 25 + 0 - 25$

Add $40 a + 25$ and $0$ .

$B a = 40 a + 25 - 25$

Subtract $25$ from $25$ .

$B a = 40 a + 0$

Add $40 a$ and $0$ .

$B a = 40 a$

Divide each term in $B a = 40 a$ by $a$ and simplify.

Divide each term in $B a = 40 a$ by $a$ .

$\frac{B a}{a} = \frac{40 a}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{B a}{a} = \frac{40 a}{a}$

Divide $B$ by $1$ .

$B = \frac{40 a}{a}$

Simplify the right side.

Cancel the common factor of $a$ .

Cancel the common factor.

$B = \frac{40 a}{a}$

Divide $40$ by $1$ .

$B = 40$

Solve for B (4a+5)^2=16a^2+Ba+25

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