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Answer :
Let's work through the problem of finding the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex] step-by-step, using the distributive property (also known as the FOIL method for binomials).
1. Multiply the first terms of each binomial:
[tex]\[(2x) \times (7) = 14x\][/tex]
2. Multiply the outer terms:
[tex]\[(2x) \times (-4x) = -8x^2\][/tex]
3. Multiply the inner terms:
[tex]\[(5) \times (7) = 35\][/tex]
4. Multiply the last terms:
[tex]\[(5) \times (-4x) = -20x\][/tex]
5. Combine all these results together:
[tex]\[-8x^2 + 14x + 35 - 20x\][/tex]
6. Combine like terms:
[tex]\[14x - 20x = -6x\][/tex]
So, the quadratic expression formed by multiplying the given factors is:
[tex]\[-8x^2 - 6x + 35\][/tex]
Therefore, the correct answer from the multiple-choice options is:
[tex]\[C. -8x^2 - 6x + 35\][/tex]
1. Multiply the first terms of each binomial:
[tex]\[(2x) \times (7) = 14x\][/tex]
2. Multiply the outer terms:
[tex]\[(2x) \times (-4x) = -8x^2\][/tex]
3. Multiply the inner terms:
[tex]\[(5) \times (7) = 35\][/tex]
4. Multiply the last terms:
[tex]\[(5) \times (-4x) = -20x\][/tex]
5. Combine all these results together:
[tex]\[-8x^2 + 14x + 35 - 20x\][/tex]
6. Combine like terms:
[tex]\[14x - 20x = -6x\][/tex]
So, the quadratic expression formed by multiplying the given factors is:
[tex]\[-8x^2 - 6x + 35\][/tex]
Therefore, the correct answer from the multiple-choice options is:
[tex]\[C. -8x^2 - 6x + 35\][/tex]
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