Respuesta :
Answer:
(A)
Step-by-step explanation:
The given expression is:
[tex]3p+12m+8[/tex]
Solving the above given expression, we have
[tex]3(p+4m)+8[/tex]
Now, A. The given expression is:
[tex]3(p+4m)+8[/tex] which is as same as the given expression, thus this option is correct.
B. The given expression is:
[tex]3(3p+4m+8)[/tex]
=[tex]9p+12m+24[/tex]
which is not equivalent to the given expression, thus this option is incorrect.
C.The given expression is:
[tex]9p+3m+2[/tex]
=[tex]3(3p+m)+2[/tex]
which is not equivalent to the given expression, thus this option is incorrect.
D. The given expression is:
[tex]8+12(m+3p)[/tex]
which is not equivalent to the given expression, thus this option is incorrect.
The correct option is [tex]\boxed{\bf option (a)}[/tex].
Further explanation:
An expression is the combination of symbols which are numbers (constants), operations, variables, functions, brackets and punctuation
A constant is a known value in an expression.
A variable is an unknown quantity in the expression.
The given expression is [tex]3p+12m+8[/tex] where [tex]p\text{ and }m[/tex] are unknown quantities.
Option (a)
Here, the option is [tex]3(p+4m)+8[/tex].
Now, simplify the above expression as follows:
[tex]\begin{aligned}3(p+4m)+8&=3p+(3\cdot 4)m+8\\&=3p+12m+8\end{aligned}[/tex]
The above obtained expression is same as the given expression [tex]3p+12m+8[/tex].
Therefore, option (a) is correct.
Option (b)
Here, the option is [tex]3(p+4m+8)[/tex].
Now, simplify the above expression as follows:
[tex]\begin{aligned}3(p+4m+8)&=(3\cdot 3)p+(3\cdot 4)m+(3\cdot 8)\\&=9p+12m+24\end{aligned}[/tex]
The above obtained expression is not same as the given expression [tex]3p+12m+8[/tex].
Therefore, option (b) is incorrect.
Option (c)
Here, the option is [tex]9p+3m+2[/tex].
The above expression is already in the simplest form.
The above expression is not same as the given expression [tex]3p+12m+8[/tex].
Therefore, option (c) is incorrect.
Option (d)
Here, the option is [tex]8+12(m+3p)[/tex].
Now, simplify the above expression as follows:
[tex]\begin{aligned}8+12(m+3p)&=8+12m+(12\cdot 3)p\\&=36p+12m+8\end{aligned}[/tex]
The above obtained expression is not same as the given expression [tex]3p+12m+8[/tex].
Therefore, option (d) is incorrect.
Thus, the correct option is [tex]\boxed{\bf option (a)}[/tex].
Learn more
1. Problem on the whole numbers are positive integers https://brainly.com/question/1852063.
2. Problem on the adding and simplifying the numbers https://brainly.com/question/894273.
3. Problem on the general form of the equation of the circle https://brainly.com/question/1506955.
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Polynomials
Keywords: Expression, symbols, constants, variables, operations, punctuation, Multiplication, division, addition, subtraction, linear polynomial, quadratic polynomial, prime numbers.
