Đáp án:
$a) (x + 3)² + 2(x + 3)(x – 2) + (x – 2)²$
$= x^{2} + 2x3 + 3^{2} + 2x^{2} - 4x + 6x - 12 + x^{2} - 2x2 + 2^{2}$
$= x^{2} + 6x + 9 + 2x^{2} - 4x + 6x - 12 + x^{2} - 4x + 4$
$= (x^{2} + 2x^{2} + x^{2}) + (6x - 4x + 6x - 4x) + (9 - 12 + 4)$
$= 4x^{2} + 4x + 1$
$= (2x)^{2} + 2.2x.1 + 1$
$= (2x + 1)^{2}$
$b) (x + 4)² – 2(x + 4)(x – 3) + (x – 3)²$
$= x^{2} + 2x4 + 4^{2} - (2x^{2} - 6x + 8x - 24) + x^{2} - 2x3 + 3^{2}$
$= x^{2} + 8x + 16 - 2x^{2} + 6x - 8x + 24 + x^{2} - 6x + 9$
$= (x^{2} - 2x^{2} + x^{2}) + (8x + 6x - 8x - 6x) + (16 + 24 + 9)$
$= 0 + 0 + 49$
$= 49$
