To simplify the given expression [tex]\(4x(3x - 7) - 19x^2\)[/tex], follow these steps:
### Step 1: Distribute the [tex]\(4x\)[/tex] across the terms inside the parentheses
First, apply the distributive property to [tex]\(4x(3x - 7)\)[/tex]:
[tex]\[ 4x \cdot 3x - 4x \cdot 7 \][/tex]
- Multiplying [tex]\(4x\)[/tex] by [tex]\(3x\)[/tex] yields [tex]\(12x^2\)[/tex]
- Multiplying [tex]\(4x\)[/tex] by [tex]\(-7\)[/tex] yields [tex]\(-28x\)[/tex]
So, the expression becomes:
[tex]\[ 12x^2 - 28x \][/tex]
### Step 2: Subtract the [tex]\(19x^2\)[/tex]
Now, we need to incorporate the [tex]\(-19x^2\)[/tex] term. The expression so far is:
[tex]\[ 12x^2 - 28x - 19x^2 \][/tex]
### Step 3: Combine like terms
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 12x^2 - 19x^2 \][/tex]
This simplifies to:
[tex]\[ (12 - 19)x^2 = -7x^2 \][/tex]
So the combined expression now is:
[tex]\[ -7x^2 - 28x \][/tex]
### Final Simplified Expression
The simplified form of the given expression [tex]\(4x(3x - 7) - 19x^2\)[/tex] is:
[tex]\[\boxed{-7x^2 - 28x}\][/tex]
