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Sagot :
The expression is equivalent to 2(a + 2b) minus a minus 2b expression and gives the same result as the given expression is [tex]a+2b[/tex].
What is equivalent expression?
Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.
Given information-
The given expression in the problem is,
[tex]2 (a+ 2 b)-a-2b[/tex]
Let the expression which is equal to the given expression is [tex]f(a,b)[/tex]. Thus,
[tex]f(a,b)=2 (a+ 2 b)-a-2b[/tex]
In the above expression the term inside the bracket is in multiple with the number two.
Thus open the bracket by multiplying each term inside the bracket with number 2 as,
[tex]f(a,b)=2\times a+ 2\times2 b-a-2b\\f(a,b)=2a+4b-a-2b[/tex]
In the algebraic expression the term with same coefficient or variable added or subtract from each other.
In the above expression the solve the term a and b separately as,
[tex]f(a,b)=2a-a+4b-2b\\f(a,b)=a+2b[/tex]
Thus the expression is equivalent to given expression and gives the same result as the given expression is [tex]a+2b[/tex].
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
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