Solve (3m - 2n) ^ 2 + (2m - 3n) ^ 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

$$(3m-2n)^{2}+(2m-3n)^{2}$$

Evaluate

$13m^{2}-24mn+13n^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(3m-2n\right)^{2}$.

$$9m^{2}-12mn+4n^{2}+\left(2m-3n\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2m-3n\right)^{2}$.

$$9m^{2}-12mn+4n^{2}+4m^{2}-12mn+9n^{2}$$

Combine $9m^{2}$ and $4m^{2}$ to get $13m^{2}$.

$$13m^{2}-12mn+4n^{2}-12mn+9n^{2}$$

Combine $-12mn$ and $-12mn$ to get $-24mn$.

$$13m^{2}-24mn+4n^{2}+9n^{2}$$

Combine $4n^{2}$ and $9n^{2}$ to get $13n^{2}$.

$$13m^{2}-24mn+13n^{2}$$

Expand

$13m^{2}-24mn+13n^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(3m-2n\right)^{2}$.

$$9m^{2}-12mn+4n^{2}+\left(2m-3n\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2m-3n\right)^{2}$.

$$9m^{2}-12mn+4n^{2}+4m^{2}-12mn+9n^{2}$$

Combine $9m^{2}$ and $4m^{2}$ to get $13m^{2}$.

$$13m^{2}-12mn+4n^{2}-12mn+9n^{2}$$

Combine $-12mn$ and $-12mn$ to get $-24mn$.

$$13m^{2}-24mn+4n^{2}+9n^{2}$$

Combine $4n^{2}$ and $9n^{2}$ to get $13n^{2}$.

$$13m^{2}-24mn+13n^{2}$$