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Expression 4 (3n - 5) is equivalent to C: 12n - 20

Further explanation

Algebraic expressions in mathematics are a combination of coefficients, numbers, variables, constants and arithmetic operations such as addition, subtraction, multiplication, and division.

The main composition of algebraic expressions are:

  • 1. phrases

algebraic forms separated by arithmetic operations

consists of one phrase (monomial) to many phrases (polynomial)

  • 2. variable

is a value that can be changed, can be in the form of letters, for example, x, y, a, b, etc.

  • 3. constants

is a fixed value, can be a number

  • 4. arithmetic operations  ⇒ +, - , : , x

Calculation operations include multiply, divide, add, substract, etc.

There are several properties in integer multiplication operations

  • 1. closed property

Multiplication between integers will produce integers too

  • 2. commutative property

a x b = b x a

  • 3. associative property

ax (bxc) = (axb) xc

  • 4. identity

ax1 = 1 x a = a

  • 5. distributive  property

* addition

ax (b + c) = axb + axc

* substraction

ax (b-c) = axb - axc

We can use distributive  property  of substraction   to solve the problem

[tex]\displaystyle =4(3n-5)\\\\=4x3n - 4x5\\\\=12n-20[/tex]

"Equivalent to" means having the same value.

From the answer choices , which produce the same expression is C. 12n-20

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Keywords: PEMDAS, arithmetic operations, multiply, Parentheses, equivalent to

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The expression that is equivalent to [tex]4\left( {3n - 5} \right)[/tex] is [tex]\boxed{12n - 20}[/tex]. Option (C) is correct.

Further explanation:

To solve the grouping of multiplication, addition, subtraction and division always use the PEDMAS rule.

P represents the parenthesis, E represents exponents, M represents multiplication, D represents division, A represents addition and S represents subtraction.

Given:

The options are as follows,

A. [tex]7\text{n} - 20[/tex]

B. [tex]12\text{n} - 5[/tex]

C. [tex]12\text{n} - 5[/tex]

D. [tex]7\text{n} - 9[/tex]

Explanation:

The given expression is [tex]4\left( {3n - 5} \right).[/tex]

Consider the expression as [tex]\text{A}[/tex].

[tex]A = 4\left( {3n - 5} \right)[/tex]

Solve the expression [tex]A = 4\left( {3n - 5} \right)[/tex] to obtain the equivalent expression.

[tex]\begin{aligned}A &= 4\left( {3n - 5} \right)\\&= 4 \times 3n - 4 \times 5\\&= 12n- 20\\\end{aligned}[/tex]

The expression that is equivalent to [tex]4\left( {3n - 5} \right)[/tex] is [tex]\boxed{12n - 20}[/tex]. Option (C) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is correct.

Option (D) is not correct.

Learn more

  1. Learn more about the polynomial https://brainly.com/question/12996944
  2. Learn more about logarithm model https://brainly.com/question/13005829
  3. Learn more about the product of binomial and trinomial https://brainly.com/question/1394854

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: expression, equivalent, division, equation, multiplication, exponents, parenthesis.

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