Solve (z - b) ^ 2 + (z + b) ^ 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

$$(z-b)^{2}+(z+b)^{2}$$

Evaluate

$2\left(z^{2}+b^{2}\right)$

Solution Steps

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

$$z^{2}-2zb+b^{2}+\left(z+b\right)^{2}$$

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

$$z^{2}-2zb+b^{2}+z^{2}+2zb+b^{2}$$

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

$$2z^{2}-2zb+b^{2}+2zb+b^{2}$$

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

$$2z^{2}+b^{2}+b^{2}$$

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

$$2z^{2}+2b^{2}$$

Expand

$2z^{2}+2b^{2}$

Solution Steps

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

$$z^{2}-2zb+b^{2}+\left(z+b\right)^{2}$$

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

$$z^{2}-2zb+b^{2}+z^{2}+2zb+b^{2}$$

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

$$2z^{2}-2zb+b^{2}+2zb+b^{2}$$

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

$$2z^{2}+b^{2}+b^{2}$$

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

$$2z^{2}+2b^{2}$$