Solve -(m+7)(m-1)+4(2m+1)(3m-4)

$$- ( m + 7 ) ( m - 1 ) + 4 ( 2 m + 1 ) ( 3 m - 4 )$$

Evaluate

$$23m^{2}-26m-9$$

Solution Steps

To find the opposite of m+7, find the opposite of each term.

$$\left(-m-7\right)\left(m-1\right)+4\left(2m+1\right)\left(3m-4\right)$$

Apply the distributive property by multiplying each term of -m-7 by each term of m-1.

$$-m^{2}+m-7m+7+4\left(2m+1\right)\left(3m-4\right)$$

Combine m and -7m to get -6m.

$$-m^{2}-6m+7+4\left(2m+1\right)\left(3m-4\right)$$

Use the distributive property to multiply 4 by 2m+1.

$$-m^{2}-6m+7+\left(8m+4\right)\left(3m-4\right)$$

Apply the distributive property by multiplying each term of 8m+4 by each term of 3m-4.

$$-m^{2}-6m+7+24m^{2}-32m+12m-16$$

Combine -32m and 12m to get -20m.

$$-m^{2}-6m+7+24m^{2}-20m-16$$

Combine -m^{2} and 24m^{2} to get 23m^{2}.

$$23m^{2}-6m+7-20m-16$$

Combine -6m and -20m to get -26m.

$$23m^{2}-26m+7-16$$

Subtract 16 from 7 to get -9.

$$23m^{2}-26m-9$$

Expand

$$23m^{2}-26m-9$$

Solution Steps

To find the opposite of m+7, find the opposite of each term.

$$\left(-m-7\right)\left(m-1\right)+4\left(2m+1\right)\left(3m-4\right)$$

Apply the distributive property by multiplying each term of -m-7 by each term of m-1.

$$-m^{2}+m-7m+7+4\left(2m+1\right)\left(3m-4\right)$$

Combine m and -7m to get -6m.

$$-m^{2}-6m+7+4\left(2m+1\right)\left(3m-4\right)$$

Use the distributive property to multiply 4 by 2m+1.

$$-m^{2}-6m+7+\left(8m+4\right)\left(3m-4\right)$$

Apply the distributive property by multiplying each term of 8m+4 by each term of 3m-4.

$$-m^{2}-6m+7+24m^{2}-32m+12m-16$$

Combine -32m and 12m to get -20m.

$$-m^{2}-6m+7+24m^{2}-20m-16$$

Combine -m^{2} and 24m^{2} to get 23m^{2}.

$$23m^{2}-6m+7-20m-16$$

Combine -6m and -20m to get -26m.

$$23m^{2}-26m+7-16$$

Subtract 16 from 7 to get -9.

$$23m^{2}-26m-9$$