Break down the expression into basic terms: $$ 3x^2 + 2x $$

$$ 3\cdot x^2 + x + 2\cdot x $$

Break down the expression into basic terms: $$ 4x^2 + 3x $$

$$ $$$$ 7\cdot x\cdot x\cdot x $$

Rewrite using basic components: $$ 6z^2 + z $$

$$ 6\cdot z\cdot z + 1\cdot z $$

Simplify the expression: $$ 5x^3 + 3x^2 $$

$$ 5\cdot x\cdot x\cdot x + 3\cdot x\cdot x $$

$$ 5x^2 \cdot x + 3x \cdot x $$

Break down the expression into basic terms: $$ 3y^2 + 6 $$

$$ 3\cdot y\cdot y \cdot 2 + 6 $$

Factorization: Common factor extraction - Examples, Exercises and Solutions

Understanding Factorization: Common factor extraction

Complete explanation with examples

Factorization

The factorization we do by extracting the common factor is our way of modifying the way the exercise is written, that is, from an expression with addition to an expression with multiplication.

For example, the expression
$2A + 4B$
is composed of two terms and a plus sign. We can factor it by excluding the largest common term.
In this case it is $2$ .

We will write it as follows:
$2A + 4B = 2\times (A + 2B)$

Since both terms ( $A$ and $B$ ) were multiplied by $2$ we could "extract" it. The remaining expression is written in parentheses and the common factor (the $2$ ) is kept out.
In this way we went from having two terms in an addition operation to having a multiplication. This procedure is called factorization.

You can also apply the distributive property to do a reverse process as needed.
In certain cases we will prefer to have a multiplication and in others an addition.

Detailed explanation

Practice Factorization: Common factor extraction

Test your knowledge with 36 quizzes

Break down the expression into basic terms:

$$ 5x^2 + 10 $$

Examples with solutions for Factorization: Common factor extraction

Step-by-step solutions included

Exercise #1

Break down the expression into basic terms:

$2x^2$

Step-by-Step Solution

The expression $2x^2$ can be factored and broken down into the following basic terms:

The coefficient $2$ remains as it is since it is already a basic term.
The term $x^2$ can be broken down into $x \cdot x$ .
Therefore, the entire expression can be written as $2 \cdot x \cdot x$ .

This breakdown helps in understanding the multiplicative nature of the expression.

Among the provided choices, the correct one that matches this breakdown is choice 2: $2\cdot x\cdot x$ .

Answer:

$2\cdot x\cdot x$

Exercise #2

Break down the expression into basic terms:

$6x$

Step-by-Step Solution

To solve this problem, we'll clearly delineate the expression $6x$ as follows:

The number 6 is the coefficient.
The letter $x$ is the variable.
These two components are connected by multiplication, represented as $6 \cdot x$ .

Thus, the expression $6x$ is equivalent to $6 \cdot x$ , where 6 is multiplied by $x$ .

Examining the choice options:

Choice 1: $6\cdot x$ is correct because it represents the expression as a product of the coefficient and the variable.
Choice 2: $x \cdot x \cdot x \cdot x \cdot x \cdot x$ represents a repeated multiplication of $x$ , not applicable here.
Choice 3: $\frac{6}{x}$ represents division, not the required approach.
Choice 4: Incorrect, as $6x$ can indeed be expressed as $6 \cdot x$ .

Therefore, the best breakdown of the expression is $6 \cdot x$ , matching choice 1.

Answer:

$6\cdot x$

Exercise #3

Break down the expression into basic terms:

$5x^2$

Step-by-Step Solution

To break down the expression $5x^2$ into its basic terms, we identify each component in the expression:

$5 \, \text{is a constant multiplier}$

$x^2$ means $x \cdot x$

Therefore, $5x^2$ can be rewritten as $5 \cdot x \cdot x$ .

Answer:

$5\cdot x\cdot x$

Exercise #4

Break down the expression into basic terms:

$3y^3$

Step-by-Step Solution

To break down the expression $3y^3$ into its basic terms, we understand the components of the expression:

$3 \, \text{is a constant multiplier}$

$y^3$ can be rewritten as $y \cdot y \cdot y$

Thus, $3y^3$ can be decomposed into $3 \cdot y \cdot y \cdot y$ .

Answer:

$3\cdot y\cdot y \cdot y$

Exercise #5

Break down the expression into basic terms:

$4a^2$

Step-by-Step Solution

To break down the expression $4a^2$ into basic terms, we need to look at each factor:

$4 \, \text{is a constant multiplier}$

$a^2$ means $a \cdot a$

Hence, $4a^2$ is equivalent to $4 \cdot a \cdot a$ .

Answer:

$4\cdot a\cdot a$

More Factorization: Common factor extraction Questions

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Topics Learned in Later Sections

Algebraic Method The Extended Distributive Property

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Solving the problem Third power Applying the formula Complete the missing number Decomposing a Number into smaller numbers/parts Extracting a Common Factor from a group of numbers following decomposition Identifying a Common Factor of a number following decomposition Matching expressions equal in value Number of terms Solving the problem Third power