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Answer :
To find the product of the expressions [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex], we need to apply the distributive property (often referred to as the FOIL method for binomials, which stands for First, Outer, Inner, Last). Here's a step-by-step breakdown of the process:
1. Multiply the First terms:
- [tex]\(7x \cdot 5x = 35x^2\)[/tex]
2. Multiply the Outer terms:
- [tex]\(7x \cdot (-11) = -77x\)[/tex]
3. Multiply the Inner terms:
- [tex]\(2 \cdot 5x = 10x\)[/tex]
4. Multiply the Last terms:
- [tex]\(2 \cdot (-11) = -22\)[/tex]
5. Combine all the terms:
- [tex]\(35x^2 + (-77x) + 10x + (-22)\)[/tex]
6. Simplify by combining like terms:
- The [tex]\(x\)[/tex] terms: [tex]\(-77x + 10x = -67x\)[/tex]
Putting it all together, the simplified product is:
[tex]\[ 35x^2 - 67x - 22 \][/tex]
Therefore, the correct answer is option B: [tex]\(35x^2 - 67x - 22\)[/tex].
1. Multiply the First terms:
- [tex]\(7x \cdot 5x = 35x^2\)[/tex]
2. Multiply the Outer terms:
- [tex]\(7x \cdot (-11) = -77x\)[/tex]
3. Multiply the Inner terms:
- [tex]\(2 \cdot 5x = 10x\)[/tex]
4. Multiply the Last terms:
- [tex]\(2 \cdot (-11) = -22\)[/tex]
5. Combine all the terms:
- [tex]\(35x^2 + (-77x) + 10x + (-22)\)[/tex]
6. Simplify by combining like terms:
- The [tex]\(x\)[/tex] terms: [tex]\(-77x + 10x = -67x\)[/tex]
Putting it all together, the simplified product is:
[tex]\[ 35x^2 - 67x - 22 \][/tex]
Therefore, the correct answer is option B: [tex]\(35x^2 - 67x - 22\)[/tex].
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