Question

solve the following system of linear equations:

\\(\

$$\begin{cases} 2a + 5b = 3 \\\\ 3a - 5b = -8 \\end{cases}$$

\\)

Explanation:

🆕 New Concept Discovered: Factoring by Grouping
Grouping terms to find common binomial factors.

Step 1: Group the terms

We group the four terms into two pairs:

$$ (15x^3 + 12x^2) + (10x + 8) $$

Step 2: Factor out the GCF from each group

From the first group, \(15x^3 + 12x^2\), we factor out the greatest common factor, \(3x^2\):

$$ 3x^2(5x + 4) $$

From the second group, \(10x + 8\), we factor out the greatest common factor, \(2\):

$$ 2(5x + 4) $$

Now we rewrite the expression:

$$ 3x^2(5x + 4) + 2(5x + 4) $$

Step 3: Factor out the common binomial

Both terms now share a common binomial factor of \((5x + 4)\). We factor this out:

$$ (3x^2 + 2)(5x + 4) $$

Answer:

$$ (3x^2 + 2)(5x + 4) $$