Algebraic Method Practice Problems with Solutions

To break down the expression$4x^2 + 6x$ into its basic terms, we need to look for a common factor in both terms.

The first term is $4x^2$, which can be rewritten as $4\cdot x\cdot x$.

The second term is$6x$, which can be rewritten as $2\cdot 3\cdot x$.

The common factor between the terms is $x$.

Thus, the expression can be broken down into $4\cdot x^2 + 6\cdot x$, and further rewritten with common factors as $4\cdot x\cdot x + 6\cdot x$.

To simplify the expression $5x^3 + 3x^2$, we can break it down into basic terms:

The term $5x^3$ can be written as $5 \cdot x \cdot x \cdot x$.

The term$3x^2$ can be written as $3 \cdot x \cdot x$.

Thus, the expression simplifies to$5 \cdot x \cdot x \cdot x + 3 \cdot x \cdot x$.

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 rewrite the expression $8x^2 - 4x$ using its basic components, we'll follow these steps:

• Step 1: Identify the greatest common factor of the terms.
• Step 2: Factor each term using the greatest common factor.

Let's go through each step:

Step 1: Recognize that both terms $8x^2$ and $4x$ contain $x$ as a common factor.
Moreover, the numerical coefficients 8 and 4 have a common factor of 4.

Step 2: Factor the expression:
- $8x^2$ can be expressed as $8 \cdot x \cdot x$.
- $4x$ can be written as $4 \cdot x$.

Bringing them together, we can rewrite the expression:

$8x^2 - 4x = 8 \cdot x \cdot x - 4 \cdot x$.

Thus, the solution to the problem is $8\cdot x\cdot x-4\cdot x$.

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