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Answer :
To find the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we'll expand the expression using the distributive property. This method requires multiplying each term in the first binomial by each term in the second binomial.
Here are the steps:
1. Multiply the first terms from each binomial:
[tex]\[
2x \times 7 = 14x
\][/tex]
2. Multiply the first term of the first binomial by the second term of the second binomial:
[tex]\[
2x \times (-4x) = -8x^2
\][/tex]
3. Multiply the second term of the first binomial by the first term of the second binomial:
[tex]\[
5 \times 7 = 35
\][/tex]
4. Multiply the second terms from each binomial:
[tex]\[
5 \times (-4x) = -20x
\][/tex]
5. Now, combine all the results:
[tex]\[
14x - 8x^2 + 35 - 20x
\][/tex]
6. Combine the like terms:
- For the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]
- The constant and quadratic terms remain the same.
Putting it all together, the expanded form of the expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Thus, the correct quadratic expression is:
- A. [tex]\(-8x^2 - 6x + 35\)[/tex]
Here are the steps:
1. Multiply the first terms from each binomial:
[tex]\[
2x \times 7 = 14x
\][/tex]
2. Multiply the first term of the first binomial by the second term of the second binomial:
[tex]\[
2x \times (-4x) = -8x^2
\][/tex]
3. Multiply the second term of the first binomial by the first term of the second binomial:
[tex]\[
5 \times 7 = 35
\][/tex]
4. Multiply the second terms from each binomial:
[tex]\[
5 \times (-4x) = -20x
\][/tex]
5. Now, combine all the results:
[tex]\[
14x - 8x^2 + 35 - 20x
\][/tex]
6. Combine the like terms:
- For the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]
- The constant and quadratic terms remain the same.
Putting it all together, the expanded form of the expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Thus, the correct quadratic expression is:
- A. [tex]\(-8x^2 - 6x + 35\)[/tex]
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