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Simplify the product using FOIL:

[tex]$(2x - 7)(5x + 5)$[/tex]

A. [tex]$10x^2 + 25x - 35$[/tex]
B. [tex]$10x^2 - 45x + 35$[/tex]
C. [tex]$10x^2 - 25x - 35$[/tex]

Answer :

Sure! Let’s simplify the product [tex]\((2x - 7)(5x + 5)\)[/tex] using the FOIL method. FOIL stands for First, Outer, Inner, Last, which refers to a method for multiplying two binomials.

### Step-by-Step Solution:

1. First: Multiply the first terms of each binomial:
[tex]\[
2x \cdot 5x = 10x^2
\][/tex]

2. Outer: Multiply the outer terms:
[tex]\[
2x \cdot 5 = 10x
\][/tex]

3. Inner: Multiply the inner terms:
[tex]\[
-7 \cdot 5x = -35x
\][/tex]

4. Last: Multiply the last terms of each binomial:
[tex]\[
-7 \cdot 5 = -35
\][/tex]

Now, combine all these results:
[tex]\[
10x^2 + 10x - 35x - 35
\][/tex]

Next, combine like terms ([tex]\(10x\)[/tex] and [tex]\(-35x\)[/tex]):
[tex]\[
10x^2 + 10x - 35x - 35 = 10x^2 - 25x - 35
\][/tex]

So, the simplified expression is:
[tex]\[
\boxed{10x^2 - 25x - 35}
\][/tex]

Among the given options, [tex]\(10x^2 - 25x - 35\)[/tex] matches with:

- [tex]\(10 x^2-25 x-35\)[/tex]

This matches the third option.

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Rewritten by : Barada