Solve for B (6p+2)^2=36p^2+Bp+4

${(6 p + 2)}^{2} = 36 p^{2} + B p + 4$

Rewrite the equation as $36 p^{2} + B p + 4 = {(6 p + 2)}^{2}$ .

$36 p^{2} + B p + 4 = {(6 p + 2)}^{2}$

Simplify ${(6 p + 2)}^{2}$ .

Rewrite.

$36 p^{2} + B p + 4 = 0 + 0 + {(6 p + 2)}^{2}$

Rewrite ${(6 p + 2)}^{2}$ as $(6 p + 2) (6 p + 2)$ .

$36 p^{2} + B p + 4 = (6 p + 2) (6 p + 2)$

Expand $(6 p + 2) (6 p + 2)$ using the FOIL Method.

Apply the distributive property.

$36 p^{2} + B p + 4 = 6 p (6 p + 2) + 2 (6 p + 2)$

Apply the distributive property.

$36 p^{2} + B p + 4 = 6 p (6 p) + 6 p \cdot 2 + 2 (6 p + 2)$

Apply the distributive property.

$36 p^{2} + B p + 4 = 6 p (6 p) + 6 p \cdot 2 + 2 (6 p) + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$36 p^{2} + B p + 4 = 6 \cdot 6 p \cdot p + 6 p \cdot 2 + 2 (6 p) + 2 \cdot 2$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$36 p^{2} + B p + 4 = 6 \cdot 6 (p \cdot p) + 6 p \cdot 2 + 2 (6 p) + 2 \cdot 2$

Multiply $p$ by $p$ .

$36 p^{2} + B p + 4 = 6 \cdot 6 p^{2} + 6 p \cdot 2 + 2 (6 p) + 2 \cdot 2$

Multiply $6$ by $6$ .

$36 p^{2} + B p + 4 = 36 p^{2} + 6 p \cdot 2 + 2 (6 p) + 2 \cdot 2$

Multiply $2$ by $6$ .

$36 p^{2} + B p + 4 = 36 p^{2} + 12 p + 2 (6 p) + 2 \cdot 2$

Multiply $6$ by $2$ .

$36 p^{2} + B p + 4 = 36 p^{2} + 12 p + 12 p + 2 \cdot 2$

Multiply $2$ by $2$ .

$36 p^{2} + B p + 4 = 36 p^{2} + 12 p + 12 p + 4$

Add $12 p$ and $12 p$ .

$36 p^{2} + B p + 4 = 36 p^{2} + 24 p + 4$

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

Subtract $36 p^{2}$ from both sides of the equation.

$B p + 4 = 36 p^{2} + 24 p + 4 - 36 p^{2}$

Subtract $4$ from both sides of the equation.

$B p = 36 p^{2} + 24 p + 4 - 36 p^{2} - 4$

Combine the opposite terms in $36 p^{2} + 24 p + 4 - 36 p^{2} - 4$ .

Subtract $36 p^{2}$ from $36 p^{2}$ .

$B p = 24 p + 4 + 0 - 4$

Add $24 p + 4$ and $0$ .

$B p = 24 p + 4 - 4$

Subtract $4$ from $4$ .

$B p = 24 p + 0$

Add $24 p$ and $0$ .

$B p = 24 p$

Divide each term in $B p = 24 p$ by $p$ and simplify.

Divide each term in $B p = 24 p$ by $p$ .

$\frac{B p}{p} = \frac{24 p}{p}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{B p}{p} = \frac{24 p}{p}$

Divide $B$ by $1$ .

$B = \frac{24 p}{p}$

Simplify the right side.

Cancel the common factor of $p$ .

Cancel the common factor.

$B = \frac{24 p}{p}$

Divide $24$ by $1$ .

$B = 24$

Solve for B (6p+2)^2=36p^2+Bp+4

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