Answer:
Option C is correct.
[tex]-a^2+b^2 +2ab[/tex]
Step-by-step explanation:
Simplify: [tex]b(a+b) - a(a-b)[/tex] ......[1]
The distributive property says that:
[tex]x \cdot (y+z) = a\cdot y + x \cdot z[/tex]
Apply the distributive property to equation [1] we have;
[tex]b \cdot a + b \cdot b - (a\cdot a - a\cdot b)[/tex]
Simplify:
[tex]ba +b^2 - (a^2 -ab)[/tex]
or
[tex]ba + b^2 -a^2 + ab[/tex]
Use Commutative property:
xy =yx
then;
[tex]ab + b^2 -a^2 + ab[/tex]
Combine like terms;
[tex]b^2-a^2 +2ab[/tex]
Therefore, the simplified expression is,
[tex]-a^2+b^2 +2ab[/tex]
