Solve (2a + 1) ^ 2 + 4a(2a + 1) + 4a ^ 2 | 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

$$(2a+1)^{2}+4a(2a+1)+4a^{2}$$

Evaluate

$\left(4a+1\right)^{2}$

Solution Steps

Use binomial theorem $\left(p+q\right)^{2}=p^{2}+2pq+q^{2}$ to expand $\left(2a+1\right)^{2}$.

$$4a^{2}+4a+1+4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply $4a$ by $2a+1$.

$$4a^{2}+4a+1+8a^{2}+4a+4a^{2}$$

Combine $4a^{2}$ and $8a^{2}$ to get $12a^{2}$.

$$12a^{2}+4a+1+4a+4a^{2}$$

Combine $4a$ and $4a$ to get $8a$.

$$12a^{2}+8a+1+4a^{2}$$

Combine $12a^{2}$ and $4a^{2}$ to get $16a^{2}$.

$$16a^{2}+8a+1$$

Expand

$16a^{2}+8a+1$

Solution Steps

Use binomial theorem $\left(p+q\right)^{2}=p^{2}+2pq+q^{2}$ to expand $\left(2a+1\right)^{2}$.

$$4a^{2}+4a+1+4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply $4a$ by $2a+1$.

$$4a^{2}+4a+1+8a^{2}+4a+4a^{2}$$

Combine $4a^{2}$ and $8a^{2}$ to get $12a^{2}$.

$$12a^{2}+4a+1+4a+4a^{2}$$

Combine $4a$ and $4a$ to get $8a$.

$$12a^{2}+8a+1+4a^{2}$$

Combine $12a^{2}$ and $4a^{2}$ to get $16a^{2}$.

$$16a^{2}+8a+1$$