The factorization of [tex]$2 x+18+x y+9 y$[/tex] is:
A. [tex]$(x+2)(y+9)$[/tex]
B. [tex]$(x+9)(2+y)$[/tex]
C. [tex]$(x+y)(y+9)$[/tex]
D. [tex]$(x+y)(y+2)$[/tex]
Answer (1)
Factor the expression by grouping terms, factoring out common factors, and then factoring out the common binomial factor, resulting in $(x+9)(2+y).
Explanation
Understanding the Problem We are asked to factor the expression 2 x + 18 + x y + 9 y . We can use factoring by grouping to solve this problem.
Grouping Terms First, group the terms: ( 2 x + 18 ) + ( x y + 9 y ) .
Factoring Each Group Next, factor out the common factors from each group: 2 ( x + 9 ) + y ( x + 9 ) .
Factoring out the Common Binomial Now, factor out the common binomial factor ( x + 9 ) : ( x + 9 ) ( 2 + y ) .
Final Answer Therefore, the factorization of 2 x + 18 + x y + 9 y is ( x + 9 ) ( 2 + y ) .
Examples
Factoring expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are designing a rectangular garden and know the total area and some constraints on the dimensions, you can use factoring to find the possible lengths and widths of the garden. Factoring also helps in simplifying complex equations in physics and engineering, making calculations easier and more efficient. Understanding factoring helps in optimizing designs and solving practical problems in various fields.
