To expand the expression [tex]\((-f + 10g)(f - g)\)[/tex] and simplify it, we can follow these steps:
1. Distribute each term in the first binomial to each term in the second binomial.
We do this by using the distributive property, often called the FOIL method (First, Outer, Inner, Last):
[tex]\[( -f \cdot f ) + ( -f \cdot -g ) + ( 10g \cdot f ) + ( 10g \cdot -g )\][/tex]
2. Compute each of these multiplications:
- First term: [tex]\(-f \cdot f = -f^2\)[/tex]
- Outer term: [tex]\(-f \cdot -g = fg\)[/tex]
- Inner term: [tex]\(10g \cdot f = 10fg\)[/tex]
- Last term: [tex]\(10g \cdot -g = -10g^2\)[/tex]
3. Combine all these results:
[tex]\[
-f^2 + fg + 10fg - 10g^2
\][/tex]
4. Combine the like terms (terms involving [tex]\(fg\)[/tex]):
[tex]\[
-f^2 + (1fg + 10fg) - 10g^2
\][/tex]
Simplifying the coefficients:
[tex]\[
-f^2 + 11fg - 10g^2
\][/tex]
Therefore, the expanded form of [tex]\((-f + 10g)(f - g)\)[/tex] is:
[tex]\[
-f^2 + 11fg - 10g^2
\][/tex]
