Solve (41+3m)(21-m)-(31-2m)(1+m) | 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

$$(41+3m)(21-m)-(31-2m)(1+m)$$

Evaluate

$830-7m-m^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $41+3m$ by each term of $21-m$.

$$861-41m+63m-3m^{2}-\left(31-2m\right)\left(1+m\right)$$

Combine $-41m$ and $63m$ to get $22m$.

$$861+22m-3m^{2}-\left(31-2m\right)\left(1+m\right)$$

Apply the distributive property by multiplying each term of $31-2m$ by each term of $1+m$.

$$861+22m-3m^{2}-\left(31+31m-2m-2m^{2}\right)$$

Combine $31m$ and $-2m$ to get $29m$.

$$861+22m-3m^{2}-\left(31+29m-2m^{2}\right)$$

To find the opposite of $31+29m-2m^{2}$, find the opposite of each term.

$$861+22m-3m^{2}-31-29m-\left(-2m^{2}\right)$$

The opposite of $-2m^{2}$ is $2m^{2}$.

$$861+22m-3m^{2}-31-29m+2m^{2}$$

Subtract $31$ from $861$ to get $830$.

$$830+22m-3m^{2}-29m+2m^{2}$$

Combine $22m$ and $-29m$ to get $-7m$.

$$830-7m-3m^{2}+2m^{2}$$

Combine $-3m^{2}$ and $2m^{2}$ to get $-m^{2}$.

$$830-7m-m^{2}$$

Expand

$830-7m-m^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $41+3m$ by each term of $21-m$.

$$861-41m+63m-3m^{2}-\left(31-2m\right)\left(1+m\right)$$

Combine $-41m$ and $63m$ to get $22m$.

$$861+22m-3m^{2}-\left(31-2m\right)\left(1+m\right)$$

Apply the distributive property by multiplying each term of $31-2m$ by each term of $1+m$.

$$861+22m-3m^{2}-\left(31+31m-2m-2m^{2}\right)$$

Combine $31m$ and $-2m$ to get $29m$.

$$861+22m-3m^{2}-\left(31+29m-2m^{2}\right)$$

To find the opposite of $31+29m-2m^{2}$, find the opposite of each term.

$$861+22m-3m^{2}-31-29m-\left(-2m^{2}\right)$$

The opposite of $-2m^{2}$ is $2m^{2}$.

$$861+22m-3m^{2}-31-29m+2m^{2}$$

Subtract $31$ from $861$ to get $830$.

$$830+22m-3m^{2}-29m+2m^{2}$$

Combine $22m$ and $-29m$ to get $-7m$.

$$830-7m-3m^{2}+2m^{2}$$

Combine $-3m^{2}$ and $2m^{2}$ to get $-m^{2}$.

$$830-7m-m^{2}$$