Step-by-step explanation:
your teacher was very nice and warned you about the trap in the question.
so, really, what do we have to do ?
a full circle represents 360°.
the shaded sector is the full circle minus the white sector !
this is the same as directly calculating the shaded sector for 360-75 = 285°.
so, the area of a circle is
pi×r²
in our case
pi×20² = 400pi
the needed fraction of the whole circle is either
75/360, if we want to subtract it for the solution
or
285/360, if we want to calculate the solution directly.
both lead to the same result.
400pi×360/360 - 400pi×75/360 =
= 400pi × 285/360 = 10pi × 285/9 = 2850pi/9 =
= 316.6666666...pi ≈ 316.7pi
The difference of two squares factoring pattern states that a difference of two squares can be factored as follows:
So, whenever you recognize the two terms of a subtraction to be two squares, you can factor it as the sum of the roots multiplied by the difference of the roots.
In this case, the squares are obvious: 
is the square of 
, and 
is the square of 
So, we can factor the expression as
![(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)] - [(x+2)+(y+2)]](https://tex.z-dn.net/?f=%20%28x%2B2%29%5E2%20-%20%28y%2B2%29%5E2%20%3D%20%5B%28x%2B2%29%2B%28y%2B2%29%5D%20-%20%5B%28x%2B2%29%2B%28y%2B2%29%5D%20)
(the round parenthesis aren't necessary, I used them only to make clear the two terms)
We can simplify the expression summing like terms:
![(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)][(x+2)-(y+2)] = (x+y+4)(x-y)](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%20-%20%28y%2B2%29%5E2%20%3D%20%5B%28x%2B2%29%2B%28y%2B2%29%5D%5B%28x%2B2%29-%28y%2B2%29%5D%20%3D%20%28x%2By%2B4%29%28x-y%29%20)
2p*p= 2p^2 because when you multiply p by p it squares it, then you keep the 2 in front of it
If it's square rectangle rectangle square I can't know with out tĥe picture
