Answer :
To solve for the product of the quadratic expression [tex]\((2x + 5)(7 - 4x)\)[/tex], let's multiply these two binomials using the distributive property, often remembered as the FOIL method, which stands for First, Outer, Inner, Last:
1. First terms: Multiply the first terms of each binomial:
- [tex]\(2x \times 7 = 14x\)[/tex]
2. Outer terms: Multiply the outer terms of the binomials:
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
3. Inner terms: Multiply the inner terms of the binomials:
- [tex]\(5 \times 7 = 35\)[/tex]
4. Last terms: Multiply the last terms of each binomial:
- [tex]\(5 \times (-4x) = -20x\)[/tex]
Now, we need to combine all these results:
- Start with the [tex]\(-8x^2\)[/tex].
- The x terms [tex]\(14x - 20x = -6x\)[/tex].
- Lastly, add the constant term [tex]\(35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
Therefore, the correct choice is D: [tex]\(-8x^2 - 6x + 35\)[/tex].
1. First terms: Multiply the first terms of each binomial:
- [tex]\(2x \times 7 = 14x\)[/tex]
2. Outer terms: Multiply the outer terms of the binomials:
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
3. Inner terms: Multiply the inner terms of the binomials:
- [tex]\(5 \times 7 = 35\)[/tex]
4. Last terms: Multiply the last terms of each binomial:
- [tex]\(5 \times (-4x) = -20x\)[/tex]
Now, we need to combine all these results:
- Start with the [tex]\(-8x^2\)[/tex].
- The x terms [tex]\(14x - 20x = -6x\)[/tex].
- Lastly, add the constant term [tex]\(35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
Therefore, the correct choice is D: [tex]\(-8x^2 - 6x + 35\)[/tex].
