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Answer :
To expand the expression
[tex]$$
(2x + 5)(7 - 4x),
$$[/tex]
we use the distributive property (also known as the FOIL method). Here’s how to do it step by step:
1. Multiply the first term of the first binomial by the first term of the second binomial:
[tex]$$
2x \cdot 7 = 14x.
$$[/tex]
2. Multiply the first term of the first binomial by the second term of the second binomial:
[tex]$$
2x \cdot (-4x) = -8x^2.
$$[/tex]
3. Multiply the second term of the first binomial by the first term of the second binomial:
[tex]$$
5 \cdot 7 = 35.
$$[/tex]
4. Multiply the second term of the first binomial by the second term of the second binomial:
[tex]$$
5 \cdot (-4x) = -20x.
$$[/tex]
5. Now, combine like terms (the terms involving [tex]$x$[/tex]):
[tex]$$
14x - 20x = -6x.
$$[/tex]
6. Write the final quadratic expression:
[tex]$$
-8x^2 - 6x + 35.
$$[/tex]
Comparing with the given options, the expression that matches is:
D. [tex]$-8x^2 - 6x + 35$[/tex].
[tex]$$
(2x + 5)(7 - 4x),
$$[/tex]
we use the distributive property (also known as the FOIL method). Here’s how to do it step by step:
1. Multiply the first term of the first binomial by the first term of the second binomial:
[tex]$$
2x \cdot 7 = 14x.
$$[/tex]
2. Multiply the first term of the first binomial by the second term of the second binomial:
[tex]$$
2x \cdot (-4x) = -8x^2.
$$[/tex]
3. Multiply the second term of the first binomial by the first term of the second binomial:
[tex]$$
5 \cdot 7 = 35.
$$[/tex]
4. Multiply the second term of the first binomial by the second term of the second binomial:
[tex]$$
5 \cdot (-4x) = -20x.
$$[/tex]
5. Now, combine like terms (the terms involving [tex]$x$[/tex]):
[tex]$$
14x - 20x = -6x.
$$[/tex]
6. Write the final quadratic expression:
[tex]$$
-8x^2 - 6x + 35.
$$[/tex]
Comparing with the given options, the expression that matches is:
D. [tex]$-8x^2 - 6x + 35$[/tex].
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