Answer :
To find the equivalent expression for [tex]\(3x^2 + 5x - 7(x^2 + 4)\)[/tex], let's proceed step by step.
1. Expand the given expression:
[tex]\[3x^2 + 5x - 7(x^2 + 4)\][/tex]
2. Distribute the [tex]\(-7\)[/tex] inside the parentheses:
[tex]\[3x^2 + 5x - 7x^2 - 28\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 - 7x^2\)[/tex]
- Combine the constant terms: there is no other term to combine with [tex]\(-28\)[/tex]
- So we get:
[tex]\[3x^2 - 7x^2 + 5x - 28\][/tex]
4. This simplifies to:
[tex]\[ (3 - 7)x^2 + 5x - 28 \][/tex]
[tex]\[ -4x^2 + 5x - 28 \][/tex]
Now, let's compare the simplified expression [tex]\(-4x^2 + 5x - 28\)[/tex] with the given choices:
- Choice A: [tex]\(-4x^2 + 5x - 28\)[/tex] matches exactly with our simplified expression.
- Choice B: [tex]\(-4x^2 + 5x - 4\)[/tex] does not match.
- Choice C: [tex]\(x^2 + 28\)[/tex] does not match.
- Choice D: [tex]\(x^2 + 4\)[/tex] does not match.
Thus, the correct answer is:
[tex]\[ \boxed{-4x^2 + 5x - 28} \text{ (Choice A)} \][/tex]
1. Expand the given expression:
[tex]\[3x^2 + 5x - 7(x^2 + 4)\][/tex]
2. Distribute the [tex]\(-7\)[/tex] inside the parentheses:
[tex]\[3x^2 + 5x - 7x^2 - 28\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 - 7x^2\)[/tex]
- Combine the constant terms: there is no other term to combine with [tex]\(-28\)[/tex]
- So we get:
[tex]\[3x^2 - 7x^2 + 5x - 28\][/tex]
4. This simplifies to:
[tex]\[ (3 - 7)x^2 + 5x - 28 \][/tex]
[tex]\[ -4x^2 + 5x - 28 \][/tex]
Now, let's compare the simplified expression [tex]\(-4x^2 + 5x - 28\)[/tex] with the given choices:
- Choice A: [tex]\(-4x^2 + 5x - 28\)[/tex] matches exactly with our simplified expression.
- Choice B: [tex]\(-4x^2 + 5x - 4\)[/tex] does not match.
- Choice C: [tex]\(x^2 + 28\)[/tex] does not match.
- Choice D: [tex]\(x^2 + 4\)[/tex] does not match.
Thus, the correct answer is:
[tex]\[ \boxed{-4x^2 + 5x - 28} \text{ (Choice A)} \][/tex]
