Đáp án:
Giải thích các bước giải:
Bài 4:
a) (x + y)^2 + (x - y)^2
= x^2 + 2xy + y^2 + x^2 - 2xy + y^2
= (x^2 + x^2) + (2xy - 2xy) + (y^2 + y^2)
= 2x^2 + 2y^2
b) (x + 1)^3 - (2x + 1)(2x - 1) + x^2
= x^3 + 3x^2 + 3x + 1 - 2x^2 + 1 + x^2
= x^3 + (3x^2 - 2x^2 + x^2) + 3x + (1 + 1)
= x^3 + 2x^2 + 3x + 2
c) (x + 3)(x - 3) - (1 - x)(2x - 4)
= x^2 - 9 - (2x - 4 - 2x^2 + 4x)
= (x^2 + 2x^2) + (-2x - 4x) + (-9 + 4)
= 3x^2 - 6x - 5
d) (x^2 + 1)(x - 3) - (x - 3)(x^2 + 3x + 9)
= (x - 3) . (x^2 + 1 - x^2 - 3x - 9)
= (x - 3) . (-3x - 8)
= -3x^2 - 8x + 9x + 24
= -3x^2 + (-8x +9x) + 24
= -3x^2 + x + 24
e) 4x - (x + 3)^2 - (x - 3)(x + 3)
= 4x - (x^2 + 6x + 9) - (x^2 - 9)
= (-x^2 - x^2) + (4x - 6x) + (-9 + 9)
= -2x^2 - 2x
g) (2x - 1)(x + 1) - (x - 4)(x + 4)
= 2x^2 + 2x - x - 1 - (x^2 - 16)
= (2x^2 - x^2) + (2x - x) + (-1 + 16)
= x^2 - x + 15
h) (2x - 1)^2 + (2x + 1)^2 + 2(4x^2 - 1)
= 4x^2 - 4x + 1 + 4x^2 + 4x + 1 + 8x^2 - 2
= (4x^2 + 4x^2 + 8x^2) + (-4x + 4x) + (1 + 1 - 2)
= 16x^2
k) Thiếu đề
