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Answer :
To solve the problem, we need to distribute the 5 across each term inside the parentheses in the expression [tex]\((3x^2 + 7x - 11) \cdot 5\)[/tex]. Let's do this step-by-step:
1. Distribute the 5 to the first term:
The first term in the expression is [tex]\(3x^2\)[/tex]. Multiply this by 5:
[tex]\[
3x^2 \times 5 = 15x^2
\][/tex]
2. Distribute the 5 to the second term:
The second term is [tex]\(7x\)[/tex]. Multiply this by 5:
[tex]\[
7x \times 5 = 35x
\][/tex]
3. Distribute the 5 to the third term:
The third term is [tex]\(-11\)[/tex]. Multiply this by 5:
[tex]\[
-11 \times 5 = -55
\][/tex]
4. Combine these results to form the equivalent expression:
The terms we calculated are [tex]\(15x^2\)[/tex], [tex]\(35x\)[/tex], and [tex]\(-55\)[/tex]. Combining these, the expression becomes:
[tex]\[
15x^2 + 35x - 55
\][/tex]
This matches choice B from the given options. Therefore, the expression equivalent to [tex]\((3x^2 + 7x - 11) \cdot 5\)[/tex] is:
B) [tex]\(15x^2 + 35x - 55\)[/tex]
1. Distribute the 5 to the first term:
The first term in the expression is [tex]\(3x^2\)[/tex]. Multiply this by 5:
[tex]\[
3x^2 \times 5 = 15x^2
\][/tex]
2. Distribute the 5 to the second term:
The second term is [tex]\(7x\)[/tex]. Multiply this by 5:
[tex]\[
7x \times 5 = 35x
\][/tex]
3. Distribute the 5 to the third term:
The third term is [tex]\(-11\)[/tex]. Multiply this by 5:
[tex]\[
-11 \times 5 = -55
\][/tex]
4. Combine these results to form the equivalent expression:
The terms we calculated are [tex]\(15x^2\)[/tex], [tex]\(35x\)[/tex], and [tex]\(-55\)[/tex]. Combining these, the expression becomes:
[tex]\[
15x^2 + 35x - 55
\][/tex]
This matches choice B from the given options. Therefore, the expression equivalent to [tex]\((3x^2 + 7x - 11) \cdot 5\)[/tex] is:
B) [tex]\(15x^2 + 35x - 55\)[/tex]
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