Respuesta :
8a+4b-3a+5b
Here, take a's together & b's together,
(8a-3a) +(4b+5b)
5a+9b
So, your answer is 5a+9b
Here, take a's together & b's together,
(8a-3a) +(4b+5b)
5a+9b
So, your answer is 5a+9b
The simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
Further explanation:
The given expression is [tex]8a+4b-3a+5b[/tex].
The given expression consists of [tex]2[/tex] different variables [tex]a[/tex] and [tex]b[/tex]. These variables can take any values since, its value is not fixed.
An algebraic expressions are formed if different variables and are added, subtracted, multiplied and divided.
The given expression is obtained when the variable [tex]a[/tex] and variable [tex]b[/tex] is added and subtracted with multiplication with different integers.
In the given expression there are [tex]4[/tex] terms with each term having different coefficients.
Like terms in the given expression are those whose algebraic factors are same that is [tex]8a[/tex] and [tex]-3a[/tex] are like terms and [tex]4b[/tex] and [tex]5b[/tex] are like terms.
The given expression is a binomial since, it have two unlike terms.
To simplify the given expression first we have to identify the like and unlike terms.
The like terms are [tex]8a[/tex] and [tex]-3a[/tex] and other set of like terms are [tex]4b[/tex] and [tex]5b[/tex]
Since, [tex]a[/tex] and [tex]b[/tex] are variable and they are numbers they can be added or subtracted using distributive property.
[tex]8a[/tex] and [tex]-3a[/tex] are subtracted as follows:
[tex]\begin{aligned}8a-3b&=(8\cdot a)-(3\cdot a)\\&=(8-3)\cdot a\\&=5\cdot a\\&=5a\end{aligned}[/tex]
[tex]4b[/tex] and [tex]5b[/tex] are added as follows:
[tex]\begin{aligned}4b+5b&=(4\cdot b)+(5\cdot b)\\&=(4+5)\cdot b\\&=9\cdot b\\&=9b\end{aligned}[/tex]
Therefore, simplified form of the given expression is [tex]5a+9b[/tex] since both are positive terms.
Thus, the simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expressions
Keywords: Simplify, 8a+4b-3a+5b, expression, 5a+9b, terms, coefficients, like, unlike, addition, subtraction, variables, values, distributive property, like terms, unlike terms.
