Find the quotient. (5ab - 10b² + 15bc) ÷ 5b

Solution:

Given expression is

(5ab - 10b² + 15bc) ÷ 5b

[5ab÷ 5b] - [10b²÷ 5b] + [15bc ÷ 5b]

= 5ab/5b - 10b²/5b + 15bc/5b

= a - 2b + 3c

thus the quotient is a - 2b + 3c

Another example that is solved in a similar manner is

Divide 4a⁴b⁴ + 30a³b² + 16a²b² by 2a²b²

= (4a⁴b⁴/2a²b²) + (30a³b²/2a²b²) + ( 16a²b²/a²b²)

= (2a^{4 - 2}b^{4 - 2}) + (30a^{3 - 2}b^{2 - 2}) + (16a^{2 - 2}b^{2 - 2})

= (2a²b²) + (30a¹b⁰) + (16a⁰b⁰)

= 2a²b² + 30a + 16

Find the quotient. (5ab - 10b² + 15bc) ÷ 5b

Summary:

The quotient of (5ab - 10b² + 15bc) ÷ 5b is a - 2b + 3c.