Solve 9(2a+4b-7c)-4(b-c)-7(-c-4b)

$$9 ( 2 a + 4 b - 7 c ) - 4 ( b - c ) - 7 ( - c - 4 b )$$

Evaluate

$$18a+60b-52c$$

Solution Steps

Use the distributive property to multiply 9 by 2a+4b-7c.

$$18a+36b-63c-4\left(b-c\right)-7\left(-c-4b\right)$$

Use the distributive property to multiply -4 by b-c.

$$18a+36b-63c-4b+4c-7\left(-c-4b\right)$$

Combine 36b and -4b to get 32b.

$$18a+32b-63c+4c-7\left(-c-4b\right)$$

Combine -63c and 4c to get -59c.

$$18a+32b-59c-7\left(-c-4b\right)$$

Use the distributive property to multiply -7 by -c-4b.

$$18a+32b-59c-7\left(-c\right)+28b$$

Multiply -7 and -1 to get 7.

$$18a+32b-59c+7c+28b$$

Combine -59c and 7c to get -52c.

$$18a+32b-52c+28b$$

Combine 32b and 28b to get 60b.

$$18a+60b-52c$$

Expand

$$18a+60b-52c$$

Solution Steps

Use the distributive property to multiply 9 by 2a+4b-7c.

$$18a+36b-63c-4\left(b-c\right)-7\left(-c-4b\right)$$

Use the distributive property to multiply -4 by b-c.

$$18a+36b-63c-4b+4c-7\left(-c-4b\right)$$

Combine 36b and -4b to get 32b.

$$18a+32b-63c+4c-7\left(-c-4b\right)$$

Combine -63c and 4c to get -59c.

$$18a+32b-59c-7\left(-c-4b\right)$$

Use the distributive property to multiply -7 by -c-4b.

$$18a+32b-59c-7\left(-c\right)+28b$$

Multiply -7 and -1 to get 7.

$$18a+32b-59c+7c+28b$$

Combine -59c and 7c to get -52c.

$$18a+32b-52c+28b$$

Combine 32b and 28b to get 60b.

$$18a+60b-52c$$