\frac{8 y^2+4 y}{2 y}=
Answer (2)
Factor the numerator: 8 y 2 + 4 y = 4 y ( 2 y + 1 ) .
Rewrite the expression: 2 y 4 y ( 2 y + 1 ) .
Cancel the common factor: 2 y 4 y ( 2 y + 1 ) = 2 ( 2 y + 1 ) .
Distribute the constant: 2 ( 2 y + 1 ) = 4 y + 2 . The simplified expression is 4 y + 2 .
Explanation
Understanding the problem We are asked to simplify the expression 2 y 8 y 2 + 4 y . To do this, we will factor the numerator and then cancel any common factors with the denominator.
Factoring the numerator First, we factor the numerator. Both terms in the numerator, 8 y 2 and 4 y , have a common factor of 4 y . Factoring out 4 y from the numerator gives us 8 y 2 + 4 y = 4 y ( 2 y + 1 ) .
Canceling common factors Now we can rewrite the original expression as 2 y 4 y ( 2 y + 1 ) . We see that both the numerator and the denominator have a common factor of 2 y . We can cancel this common factor, which gives us 2 y 4 y ( 2 y + 1 ) = 1 2 ( 2 y + 1 ) = 2 ( 2 y + 1 ) .
Distributing the constant Finally, we distribute the 2 to the terms inside the parentheses: 2 ( 2 y + 1 ) = 4 y + 2 . Therefore, the simplified expression is 4 y + 2 .
Examples
In real life, simplifying algebraic expressions can help optimize resource allocation. For example, if you are managing a budget where expenses are related to a variable (like time or quantity), simplifying the expression can make it easier to understand how changes in that variable affect your overall costs. This skill is crucial in fields like finance, engineering, and project management, where efficient resource management is key to success. By understanding how to simplify expressions, you can make informed decisions and avoid unnecessary complexity in your calculations.
To simplify 2 y 8 y 2 + 4 y , first factor the numerator to get 4 y ( 2 y + 1 ) . Next, cancel the common factor 2 y from both numerator and denominator, resulting in 2 ( 2 y + 1 ) , and then distribute to obtain the final answer: 4 y + 2 .
;
