Answer :
To find the product of [tex]\((2x + 5)\)[/tex] and [tex]\((x + 7)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials). Let's break it down step-by-step.
1. First, multiply each term in the first binomial by each term in the second binomial:
[tex]\[
(2x + 5)(x + 7)
\][/tex]
2. Distribute [tex]\(2x\)[/tex] to each term in the second binomial:
- [tex]\(2x \cdot x = 2x^2\)[/tex]
- [tex]\(2x \cdot 7 = 14x\)[/tex]
3. Distribute [tex]\(5\)[/tex] to each term in the second binomial:
- [tex]\(5 \cdot x = 5x\)[/tex]
- [tex]\(5 \cdot 7 = 35\)[/tex]
4. Combine all these products:
[tex]\[
2x^2 + 14x + 5x + 35
\][/tex]
5. Combine like terms ([tex]\(14x\)[/tex] and [tex]\(5x\)[/tex]):
[tex]\[
2x^2 + 19x + 35
\][/tex]
So, the product of [tex]\((2x + 5)\)[/tex] and [tex]\((x + 7)\)[/tex] is:
[tex]\[
2x^2 + 19x + 35
\][/tex]
Hence, the correct expression from the given options is:
[tex]\[
2x^2 + 19x - 35
\][/tex]
1. First, multiply each term in the first binomial by each term in the second binomial:
[tex]\[
(2x + 5)(x + 7)
\][/tex]
2. Distribute [tex]\(2x\)[/tex] to each term in the second binomial:
- [tex]\(2x \cdot x = 2x^2\)[/tex]
- [tex]\(2x \cdot 7 = 14x\)[/tex]
3. Distribute [tex]\(5\)[/tex] to each term in the second binomial:
- [tex]\(5 \cdot x = 5x\)[/tex]
- [tex]\(5 \cdot 7 = 35\)[/tex]
4. Combine all these products:
[tex]\[
2x^2 + 14x + 5x + 35
\][/tex]
5. Combine like terms ([tex]\(14x\)[/tex] and [tex]\(5x\)[/tex]):
[tex]\[
2x^2 + 19x + 35
\][/tex]
So, the product of [tex]\((2x + 5)\)[/tex] and [tex]\((x + 7)\)[/tex] is:
[tex]\[
2x^2 + 19x + 35
\][/tex]
Hence, the correct expression from the given options is:
[tex]\[
2x^2 + 19x - 35
\][/tex]
