Answer :
To find the product of the expressions [tex]\((3x - 5)\)[/tex] and [tex]\((2x + 7)\)[/tex], we'll use the distributive property, often known as the FOIL method for binomials. Here's the step-by-step process:
1. First Terms: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
3x \times 7 = 21x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
-5 \times 7 = -35
\][/tex]
5. Combine all parts: Add together all these results:
[tex]\[
6x^2 + 21x - 10x - 35
\][/tex]
6. Simplify the expression: Combine like terms (in this case, the [tex]\(x\)[/tex] terms):
[tex]\[
6x^2 + (21x - 10x) - 35 = 6x^2 + 11x - 35
\][/tex]
Therefore, the product of [tex]\((3x - 5)\)[/tex] and [tex]\((2x + 7)\)[/tex] is [tex]\(\boxed{6x^2 + 11x - 35}\)[/tex].
Based on the choices provided, the correct answer is E. [tex]\(6x^2 + 11x - 35\)[/tex].
1. First Terms: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
3x \times 7 = 21x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
-5 \times 7 = -35
\][/tex]
5. Combine all parts: Add together all these results:
[tex]\[
6x^2 + 21x - 10x - 35
\][/tex]
6. Simplify the expression: Combine like terms (in this case, the [tex]\(x\)[/tex] terms):
[tex]\[
6x^2 + (21x - 10x) - 35 = 6x^2 + 11x - 35
\][/tex]
Therefore, the product of [tex]\((3x - 5)\)[/tex] and [tex]\((2x + 7)\)[/tex] is [tex]\(\boxed{6x^2 + 11x - 35}\)[/tex].
Based on the choices provided, the correct answer is E. [tex]\(6x^2 + 11x - 35\)[/tex].
