Find the value of the expression: y (7y + 4x) + (2x-y) ^ 2, with X = √2, y = √3.

y (7y + 4x) + (2x – y) ^ 2 – expand the brackets; the first parenthesis, by multiplying y by each term in the parenthesis, by 7y and by 4x; the second – according to the formula of the square of the difference of two expressions (a – b) ^ 2 = a ^ 2 – 2ab + b ^ 2, where a = 2x, b = y;

7y ^ 2 + 4xy + 4x ^ 2 – 4xy + y ^ 2 = (7y ^ 2 + y ^ 2) + (4xy – 4xy) + 4x ^ 2 = 8y ^ 2 + 4x ^ 2;

x = √2; y = √3; 8 * (√3) ^ 2 + 4 * (√2) ^ 2 = 8 * 3 + 4 * 2 = 24 + 8 = 32.

Answer. 32.