Algebraic Method Practice Problems with Solutions

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: $2\cdot x\cdot x$.

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.

To break down the expression $8y^2$, we identify the basic components. The expression $y^2$ is a shorthand for$y \times y$. Therefore, $8y^2$ can be decomposed as $8 \cdot y \cdot y$.

To break down the expression $3a^3$, we recognize that $a^3$ means $a \times a \times a$. Therefore, $3a^3$ can be decomposed as $3 \cdot a\cdot a\cdot a$.

To break down the expression $8y$, we can see it as the multiplication of $8$ and $y$:

$8y = 8 \cdot y$

This shows the expression as a product of two factors, $8$ and $y$.