Solve (2n + 2) ^ 2 - (2n) ^ 2 = 116 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2n+2)^{2}-(2n)^{2}=116$$

Solve for n

$n=14$

Steps for Solving Linear Equation

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(2n+2\right)^{2}$.

$$4n^{2}+8n+4-\left(2n\right)^{2}=116$$

Expand $\left(2n\right)^{2}$.

$$4n^{2}+8n+4-2^{2}n^{2}=116$$

Calculate $2$ to the power of $2$ and get $4$.

$$4n^{2}+8n+4-4n^{2}=116$$

Combine $4n^{2}$ and $-4n^{2}$ to get $0$.

$$8n+4=116$$

Subtract $4$ from both sides.

$$8n=116-4$$

Subtract $4$ from $116$ to get $112$.

$$8n=112$$

Divide both sides by $8$.

$$n=\frac{112}{8}$$

Divide $112$ by $8$ to get $14$.

$$n=14$$