1. Tính :
a, (2+xy)^2
b, (5-3x)^2
c, (5-x^2)(5+x^2)
d, (5x-1)^3
e, (2x-y)(4x^2+2xy+y^2)
f, (x+3)(x^2-3x+9)
2. Rút gọn biểu thức:
a, (x+3)(x^2-3x+9)-(54+x^3)
b, (2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)
1. Tính :
a, (2+xy)^2
b, (5-3x)^2
c, (5-x^2)(5+x^2)
d, (5x-1)^3
e, (2x-y)(4x^2+2xy+y^2)
f, (x+3)(x^2-3x+9)
2. Rút gọn biểu thức:
a, (x+3)(x^2-3x+9)-(54+x^3)
b, (2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)
Đáp án:
Bài 1 :
$a) (2+xy)^2 = (2+xy)(2+xy) = 4 +2xy+2xy+x^2y^2 = 4+4xy+x^2y^2$
$b) (5-3x)^2 = (5-3x)(5-3x) = 25 -15x-15x +9x^2 = 25-30x+9x^2$
$c) (5-x^2)(5+x^2) = 25 +5x^2-5x^2 -x^4 = 25 -x^5$
$d) (5x-1)^3 = (5x-1)(5x-1)^2 = (5x-1)(25x^2-10x+1) = 125x^3 -50x^2+5x-25x^2+10x-1 = 125x^3 -75x^2+15x -1$
$e) (2x-y)(4x^2+2xy+y^2) = 8x^3 +4x^2y+2xy^2 -4x^2y -2xy^2-y^3 = 8x^3-y^3$
$f) (x+3)(x^2-3x+9) = x^3 -3x^2+9x+3x^2-9x+27 = x^3 +27$
Bài 2 :
$a) (x+3)(x^2-3x+9) – (54+x^3) = (x^3-3x^2+9x+3x^2-9x+27) – (54+x^3) = x^3 +27 – 54-x^3 = -27$
$b) (2x+y)((4x^2-2xy+y^2) – (2x-y)(4x^2+2xy+y^2) = (8x^3-4x^2y+2xy^2-4x^2y-2xy^2+y^3) – (8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3) = 8x^3 +y^3 – (8x^3-y^3) = 8x^3+y^3 -8x^3+y^3 =2y^3$
Đáp án:
Giải thích các bước giải:
\(1/\\ a,\ (2+xy)^{2}\\ =2^{2}+2.2.xy+(xy)^{2}\\ =4+4xy+x^{2}y^{2}\\ b,\ (5-3x)^{2}\\ =5^{2}-2.5.3x+(3x)^{2}\\ =25-30x+9x^{2}\\ c,\ (5-x^{2})(5+x^{2})\\ =5^{2}-(x^{2})^{2}\\ =25-x^{4}\\ d,\ (5x-1)^{3}\\ =(5x)^{3}-3.(5x)^{2}.1+3.5x.1^{2}-1^{3}\\ =125x^{3}-75x^{2}+15x-1\\ e,\ (2x-y)(4x^{2}+2xy+y^{2})\\ =(2x)^{3}-y^{3}\\ =8x^{3}-y^{3}\\ f,\ (x+3)(x^{2}-3x+9)\\ =x^{3}+3^{3}\\ =x^{3}+27\\ 2/\\ a,\ (x+3)(x^{2}-3x+9)-(54+x^{3})\\ =x^{3}+3^{3}-54-x^{3}\\ =x^{3}+27-54-x^{3}\\ =(x^{3}-x^{3})+(27-54)\\ =(-27)\\ b,\ (2x+y)(4x^{2}-2xy+y^{2})-(2x-y)(4x^{2}+2xy+y^{2})\\ =(2x)^{3}+y^{3}-[(2x)^{3}-y^{3}]\\ =8x^{3}+y^{3}-8x^{3}+y^{3}\\ =(8x^{3}-8x^{3})+(y^{3}+y^{3})\\ =2y^{3}\)
chúc bạn học tốt!