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.
### 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.
