How to solve this math question fast

<p>20) if a > 0, x^2 + y^2 = a,abd xy = a - 10, what is (x + y)^2 in terms of A?</p>

<p>A)a - 20;
B)2a - 20;
C)2a - 10
D)3a - 20;
E)3a - 10;</p>

<p>Okay I first lets expanded (x + y)^2 , so first step should be this:</p>

<p>x^2 + 2xy + y^2;</p>

<p>We already know xy = a - 10;</p>

<p>x^2 + 2(a - 10) + y^2;
x^2 + 2a - 20 + y^2;</p>

<p>We know that a = x^2 + y^2,so we have have this -></p>

<p>x^2 + 2(x^2 + y^2) - 20 + y^2 -></p>

<p>x^2 + 2x^2 + 2y^2 - 20 + y^2 ->
3x^ + 3y^2 - 20;</p>

<p>Then I expanded the answer to see which one matches this and I got answer as D;</p>

<p>3(a) - 20 -></p>

<p>3(x^2 + y^2) - 20 -> 3x^2 + 3y^2 - 20;</p>

<p>I was able to solve this question only because I had some time left of my section time is there faster way to solve it ?</p>

<p>Given:
x²+y² = a;
xy = a-10</p>

<p>*Solve:<a href="x+y">/b</a>²; expand
x²+2xy+y²; Substitute *a
for x²+y²
a+2xy; Substitute a-10 for xy
a+2(a-10) = 3a - 20</p>

<p>^Thanks.</p>

<p>Nice work too in the equation.
I must have been thinking too complicating when solving this question.</p>