Solve (p + q) ^ 2 + (p - q) ^ 2 - 2p ^ 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

$$(p+q)^{2}+(p-q)^{2}-2p^{2}=$$

Evaluate

$2q^{2}$

Solution Steps

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

$$p^{2}+2pq+q^{2}+\left(p-q\right)^{2}-2p^{2}$$

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

$$p^{2}+2pq+q^{2}+p^{2}-2pq+q^{2}-2p^{2}$$

Combine $p^{2}$ and $p^{2}$ to get $2p^{2}$.

$$2p^{2}+2pq+q^{2}-2pq+q^{2}-2p^{2}$$

Combine $2pq$ and $-2pq$ to get $0$.

$$2p^{2}+q^{2}+q^{2}-2p^{2}$$

Combine $q^{2}$ and $q^{2}$ to get $2q^{2}$.

$$2p^{2}+2q^{2}-2p^{2}$$

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

$$2q^{2}$$

Expand

$2q^{2}$

Solution Steps

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

$$p^{2}+2pq+q^{2}+\left(p-q\right)^{2}-2p^{2}$$

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

$$p^{2}+2pq+q^{2}+p^{2}-2pq+q^{2}-2p^{2}$$

Combine $p^{2}$ and $p^{2}$ to get $2p^{2}$.

$$2p^{2}+2pq+q^{2}-2pq+q^{2}-2p^{2}$$

Combine $2pq$ and $-2pq$ to get $0$.

$$2p^{2}+q^{2}+q^{2}-2p^{2}$$

Combine $q^{2}$ and $q^{2}$ to get $2q^{2}$.

$$2p^{2}+2q^{2}-2p^{2}$$

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

$$2q^{2}$$