Solve (a + 2) ^ 2 - (a - 1) ^ 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

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

Evaluate

$6a+3$

Solution Steps

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

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

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

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

To find the opposite of $a^{2}-2a+1$, find the opposite of each term.

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

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

$$4a+4+2a-1$$

Combine $4a$ and $2a$ to get $6a$.

$$6a+4-1$$

Subtract $1$ from $4$ to get $3$.

$$6a+3$$

Expand

$6a+3$

Solution Steps

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

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

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

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

To find the opposite of $a^{2}-2a+1$, find the opposite of each term.

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

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

$$4a+4+2a-1$$

Combine $4a$ and $2a$ to get $6a$.

$$6a+4-1$$

Subtract $1$ from $4$ to get $3$.

$$6a+3$$