To simplify the expression [tex]\(-4x^2 + 2x - 5(1 + x)\)[/tex], we will follow these steps:
1. Distribute the -5 through the parentheses:
[tex]\[
-5(1 + x) = -5 \cdot 1 + (-5) \cdot x = -5 - 5x
\][/tex]
2. Substitute this back into the original expression:
[tex]\[
-4x^2 + 2x - 5 - 5x
\][/tex]
3. Combine like terms:
- The [tex]\(x\)[/tex] terms: [tex]\(2x - 5x = -3x\)[/tex]
- The constant term: [tex]\(-5\)[/tex]
4. Rewrite the expression with the combined terms:
[tex]\[
-4x^2 - 3x - 5
\][/tex]
Therefore, the expression equivalent to the given expression [tex]\( -4x^2 + 2x - 5(1 + x) \)[/tex] is:
[tex]\[
-4x^2 + (-3)x + (-5)
\][/tex]
