Answer :
To find the product of the expressions [tex]\( (7x + 2) \)[/tex] and [tex]\( (5x - 11) \)[/tex], we'll follow these steps:
1. Distribute each term in the first expression to each term in the second expression:
- Multiply [tex]\( 7x \)[/tex] with each term in [tex]\( (5x - 11) \)[/tex].
- [tex]\( 7x \times 5x = 35x^2 \)[/tex]
- [tex]\( 7x \times (-11) = -77x \)[/tex]
- Multiply [tex]\( 2 \)[/tex] with each term in [tex]\( (5x - 11) \)[/tex].
- [tex]\( 2 \times 5x = 10x \)[/tex]
- [tex]\( 2 \times (-11) = -22 \)[/tex]
2. Combine all the products from the distribution:
- The resulting expression after multiplication is:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( -77x + 10x = -67x \)[/tex]
So, the simplified expression for the product is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
From the given options, the correct answer is:
B. [tex]\( 35x^2 - 67x - 22 \)[/tex]
1. Distribute each term in the first expression to each term in the second expression:
- Multiply [tex]\( 7x \)[/tex] with each term in [tex]\( (5x - 11) \)[/tex].
- [tex]\( 7x \times 5x = 35x^2 \)[/tex]
- [tex]\( 7x \times (-11) = -77x \)[/tex]
- Multiply [tex]\( 2 \)[/tex] with each term in [tex]\( (5x - 11) \)[/tex].
- [tex]\( 2 \times 5x = 10x \)[/tex]
- [tex]\( 2 \times (-11) = -22 \)[/tex]
2. Combine all the products from the distribution:
- The resulting expression after multiplication is:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( -77x + 10x = -67x \)[/tex]
So, the simplified expression for the product is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
From the given options, the correct answer is:
B. [tex]\( 35x^2 - 67x - 22 \)[/tex]
