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

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

Evaluate

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

Solution Steps

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

$$a^{2}+2ab+b^{2}+\left(b-a\right)^{2}$$

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

$$a^{2}+2ab+b^{2}+b^{2}-2ba+a^{2}$$

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

$$a^{2}+2ab+2b^{2}-2ba+a^{2}$$

Combine $2ab$ and $-2ba$ to get $0$.

$$a^{2}+2b^{2}+a^{2}$$

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

$$2a^{2}+2b^{2}$$

Expand

$2a^{2}+2b^{2}$

Solution Steps

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

$$a^{2}+2ab+b^{2}+\left(b-a\right)^{2}$$

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

$$a^{2}+2ab+b^{2}+b^{2}-2ba+a^{2}$$

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

$$a^{2}+2ab+2b^{2}-2ba+a^{2}$$

Combine $2ab$ and $-2ba$ to get $0$.

$$a^{2}+2b^{2}+a^{2}$$

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

$$2a^{2}+2b^{2}$$