3(2n - 9)
We will solve the problems associated with the distributive property of multiplication.
The Problem:
Which expression is equivalent to 6n - 27?
Solution:
Recall that,
[tex]\boxed{ \ a \cdot (b + c) = (a \cdot b) + (a \cdot c) \ }[/tex]
[tex]\boxed{ \ a \cdot (b - c) = (a \cdot b) - (a \cdot c) \ }[/tex]
Let us check one by one of the available options.
Option A
[tex]\boxed{ \ 3(2n - 9) = (3\cdot 2n) - (3 \cdot 9) \ }[/tex]
[tex]\boxed{ \ 3(2n - 9) = 6n - 27 \ }[/tex]
Option B
[tex]\boxed{ \ 6(n - 4) = (6\cdot n) - (6 \cdot 4) \ }[/tex]
[tex]\boxed{ \ 3(2n - 9) = 6n - 24 \ }[/tex]
Option C
[tex]\boxed{ \ 3(n - 9) = (3\cdot n) - (3 \cdot 9) \ }[/tex]
[tex]\boxed{ \ 3(n - 9) = 3n - 27 \ }[/tex]
Option D
[tex]\boxed{ \ 9(n - 3) = (9\cdot n) - (9 \cdot 3) \ }[/tex]
[tex]\boxed{ \ 9(n - 3) = 9n - 27 \ }[/tex]
Thus, the expression of 3(2n - 9) is equivalent to 6n - 27.
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Notes
[tex]\boxed{ \ 6n - 27 = (3 \cdot 2n) - (3 \cdot 9) \ }[/tex]
[tex]\boxed{\boxed{ \ 6n - 27 = 3(2n - 9) \ }}[/tex]
Keywords: which, expression, equivalent to, 6n - 27, distributive property, multiplication, 3(2n-9)
[tex]\boxed{3\left( {2n - 9} \right)}[/tex] is the equivalent expression for [tex]6n - 27[/tex]. Option (a) is correct.
Further explanation:
The associative property is defined as a grouping of multiplication, addition, subtraction and division.
Always use the PEDMAS rule to solve the grouping of multiplication, addition, subtraction and division.
Here, P is parenthesis, E is exponents, M is multiplication, D is division, A is addition and S is subtraction.
Given:
The options are as follows,
A. [tex]3\left( {2n - 9} \right)[/tex]
B. [tex]6\left( {n - 4} \right)[/tex]
C. [tex]3\left( {n - 9} \right)[/tex]
D. [tex]9\left( {n - 3} \right)[/tex]
Explanation:
The given expression is [tex]6n - 27.[/tex]
[tex]P = 6n - 27[/tex]
The common factor between 6 and 27 is 3.
Take 3 common from 6 and 27.
[tex]\begin{aligned}P &= 6n - 27\\&= 3 \times 2n - 3 \times 9\\&= 3\left( {2n - 9} \right)\\\end{aligned}[/tex]
[tex]\boxed{3\left( {2n - 9} \right)}[/tex] is the equivalent expression for [tex]6n - 27.[/tex] Option (a) is correct.
Option (a) is correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is not correct.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: expression, equivalent, division, equation, multiplication, exponents, parenthesis.
