Sure! Let's expand the given expression step-by-step.
The given expression is:
[tex]\[
(6 - 5x) \left(3 - \overline{7x - 5} \right)
\][/tex]
First, simplify the expression inside the parenthesis:
[tex]\[
3 - (7x - 5)
\][/tex]
This simplifies to:
[tex]\[
3 - 7x + 5 = 8 - 7x
\][/tex]
Now, substitute this back into the original expression:
[tex]\[
(6 - 5x)(8 - 7x)
\][/tex]
Next, we apply the distributive property (also known as the FOIL method for binomials) to expand the expression:
1. Multiply the first terms:
[tex]\[
6 \cdot 8 = 48
\][/tex]
2. Multiply the outer terms:
[tex]\[
6 \cdot (-7x) = -42x
\][/tex]
3. Multiply the inner terms:
[tex]\[
-5x \cdot 8 = -40x
\][/tex]
4. Multiply the last terms:
[tex]\[
-5x \cdot (-7x) = 35x^2
\][/tex]
Now, combine all these terms together:
[tex]\[
48 - 42x - 40x + 35x^2
\][/tex]
Finally, combine the like terms:
[tex]\[
35x^2 - 82x + 48
\][/tex]
So, the expanded form of [tex]\((6 - 5x) \left(3 - (7x - 5) \right)\)[/tex] is:
[tex]\[
35x^2 - 82x + 48
\][/tex]
