Sure, let's simplify the given expression step by step.
Given expression:
[tex]\[ 5x^2 + x - 4x - 6x^2 \][/tex]
Step 1: Combine like terms.
We start by identifying the like terms in the expression:
- There are [tex]\(5x^2\)[/tex] and [tex]\(-6x^2\)[/tex], which are terms that involve [tex]\(x^2\)[/tex].
- There are [tex]\(x\)[/tex] and [tex]\(-4x\)[/tex], which are terms that involve [tex]\(x\)[/tex].
Step 2: Simplify the terms involving [tex]\(x^2\)[/tex].
Combine [tex]\(5x^2\)[/tex] and [tex]\(-6x^2\)[/tex]:
[tex]\[ 5x^2 - 6x^2 = -x^2 \][/tex]
Step 3: Simplify the terms involving [tex]\(x\)[/tex].
Combine [tex]\(x\)[/tex] and [tex]\(-4x\)[/tex]:
[tex]\[ x - 4x = -3x \][/tex]
Step 4: Combine the simplified terms.
Now that we have simplified each type of term, we combine them:
[tex]\[ -x^2 - 3x \][/tex]
Step 5: Factor the simplified expression.
We can factor out a common factor of [tex]\(-x\)[/tex] from the expression:
[tex]\[ -x^2 - 3x = -x(x + 3) \][/tex]
So, the simplified form of [tex]\(5x^2 + x - 4x - 6x^2\)[/tex] is:
[tex]\[ x(-x - 3) \][/tex]
This is the final simplified expression.
