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Answer :
To find the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex], we can use the distributive property, often referred to as the FOIL method for binomials. The FOIL method consists of multiplying each term in the first binomial by each term in the second binomial:
1. First terms: Multiply the first terms in each binomial: [tex]\(7x \times 5x = 35x^2\)[/tex].
2. Outer terms: Multiply the outer terms of the binomials: [tex]\(7x \times -11 = -77x\)[/tex].
3. Inner terms: Multiply the inner terms of the binomials: [tex]\(2 \times 5x = 10x\)[/tex].
4. Last terms: Multiply the last terms in each binomial: [tex]\(2 \times -11 = -22\)[/tex].
Now, combine all these results to write the expression for the product:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Next, combine the like terms (the terms involving [tex]\(x\)[/tex]):
[tex]\[
35x^2 + (-77x + 10x) - 22 = 35x^2 - 67x - 22
\][/tex]
Thus, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
This matches option (B) in the given choices. So, the correct answer is:
(B) [tex]\(35x^2 - 67x - 22\)[/tex]
1. First terms: Multiply the first terms in each binomial: [tex]\(7x \times 5x = 35x^2\)[/tex].
2. Outer terms: Multiply the outer terms of the binomials: [tex]\(7x \times -11 = -77x\)[/tex].
3. Inner terms: Multiply the inner terms of the binomials: [tex]\(2 \times 5x = 10x\)[/tex].
4. Last terms: Multiply the last terms in each binomial: [tex]\(2 \times -11 = -22\)[/tex].
Now, combine all these results to write the expression for the product:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Next, combine the like terms (the terms involving [tex]\(x\)[/tex]):
[tex]\[
35x^2 + (-77x + 10x) - 22 = 35x^2 - 67x - 22
\][/tex]
Thus, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
This matches option (B) in the given choices. So, the correct answer is:
(B) [tex]\(35x^2 - 67x - 22\)[/tex]
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