SOLUTION: Completing the square 1. X^4+64y^4 2. X^4+y^2+25 3. X^4-11x^2y^2+y^4 Please do help me, My teacher's solution goes like this, and I didn't even understand cuz he's too f

Question 892919: Completing the square
1. X^4+64y^4
2. X^4+y^2+25
3. X^4-11x^2y^2+y^4

Please do help me,
My teacher's solution goes like this, and I didn't even understand cuz he's too fast.
Ex. x^4+2x^2y^2+9y^4
x^4+9y^4+2x^2y^2
x^4+2x^2(3y^2)+9y^4+2x^2y^2-2x^2(3y^2)
X^4+6x^2y^2+9y^4+2x^2y^2-6x^2y^2
(x^2+3y^2)^2-4x^2y^2
(x^2+3y^2)^2-(2xy)^2
(x^2+3y^2+2xy)(x^2+3y^2-2xy)

Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
1. X^4+64y^4
3. X^4-11x^2y^2+y^4
1.(X^2)^2+(8y^2)^2 +2X^2.8Y^2-2X^2.8y^2 by adding and subtracting equal values
by formula
(x^2+8y^2)^2-16X^2y^2
(x^2+8y^2)^2-(4Xy)^2 we know identity A^2-B^2=(A-B)(A+B)
(x^2+8y^2-4Xy)(x^2+8y^2+4Xy)
3. X^4-11x^2y^2+y^4
(X^2)^2+(Y^2)2-2X^2y^2+2X^2Y^2-11x^2 y^2
(X^2-Y^2)^2-9X^2 Y^2
(X^2-Y^2)^2-(3X Y)^2
(X^2-Y^2-3X Y)(X^2-Y^2+3X Y)

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