To simplify the expression [tex]\((x-7)(6x-3)\)[/tex], we need to use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand the product.
1. First: Multiply the first terms in each binomial.
[tex]\[
x \cdot 6x = 6x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials.
[tex]\[
x \cdot (-3) = -3x
\][/tex]
3. Inner: Multiply the inner terms in the binomials.
[tex]\[
-7 \cdot 6x = -42x
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
-7 \cdot (-3) = 21
\][/tex]
Now, we need to sum these products:
[tex]\[
6x^2 - 3x - 42x + 21
\][/tex]
Combine the like terms ([tex]\(-3x\)[/tex] and [tex]\(-42x\)[/tex]):
[tex]\[
6x^2 - 45x + 21
\][/tex]
Thus, the simplified expression is:
[tex]\[
6x^2 - 45x + 21
\][/tex]
So the correct answer is:
[tex]\[
\boxed{6x^2 - 45x + 21}
\][/tex]
The correct answer chooses option B:
[tex]\[
\boxed{B}
\][/tex]
