a) (x-y) ( x+ y) – (x – y) ^2 + ( x+ y)^2
b) (x + 3) ( x^2 – 3x +1)^9
c) (x – 5) ( x^2 – 5x + 25)
d) ( 2x – 1) ( 4x^2 + 2x + 1) – 4x (2x^2 -1)
a) (x-y) ( x+ y) – (x – y) ^2 + ( x+ y)^2 b) (x + 3) ( x^2 – 3x +1)^9 c) (x – 5) ( x^2 – 5x + 25) d) ( 2x – 1) ( 4x^2 + 2x + 1) – 4x (2x^2 -1)
By Autumn
$a)(x-y)(x+y)-(x-y)^2+(x+y)^2_{}$
$⇔x^2-y^2-(x^2-2xy+y^2)+x^2+2xy+y^2_{}$
$⇔x^2-x^2+2xy-y^2+x^2+2xy_{}$
$⇔4xy-y^2+x^2_{}$
$c)(x-5)(x^2+5x+25)_{}$
$⇔x^3-5^3_{}$
$⇔x^3-125_{}$
$d)(2x-1)(4x^2+2x+1)-4x(2x^2-1)_{}$
$⇔8x^3-1-8x^3+4x_{}$
$⇔4x-1_{}$
Đáp án:
Giải thích các bước giải:
a) $(x-y) ( x+ y) – (x – y)^2 + ( x+ y)^2$
$=x^2 -y^2 -(x^2 -2xy+y^2) +(x^2+2xy+y^2)$
$=x^2 -y^2 -x^2 +2xy -y^2 +x^2+2xy+y^2$
$=x^2+4xy -y^2$
b)$ (x + 3) ( x^2 – 3x +1)^9$
đề sai chăng.
c) sửa chút chỗ -5x thành 5x
$(x – 5) ( x^2 + 5x + 25)$
$=x^3 -125$
d) $( 2x – 1) ( 4x^2 + 2x + 1) – 4x (2x^2 -1)$
$=8x^3 -1 -8x^3 +4x$
$=4x-1$