rút gọn các biểu thức sau 1 cách nhanh nhất
a) (6x – 2)^2 + (2 – 5x)^2 + 2(6x – 2) (2 – 5x)
b) (2a^2 + 2a + 1) (2a^2 – 2a + 1) – (2a^2 + 1)^2
c) (x + 3) (x^2 – 3x + 9) – (54 + x^3)
d) (2x + y) (4x^2 – 2xy + y^2) – (2x – y) (4x^2 + 2xy + y^2)
e) (a + b)^2 – (a – b)^2
f) (a + b)^3 – (a – b)^3 – 2b^3
`a, (6x – 2)^2 + (2 – 5x)^2 + 2(6x – 2) (2 – 5x)`
`=(6x-2+2-5x)^2=x^2`
`b, (2a^2 + 2a + 1) (2a^2 – 2a + 1) – (2a^2 + 1)^2`
`=(2a^2+1)^2-4a^2 – (2a^2 + 1)^2=-4a^2`
`c,(x + 3) (x^2 – 3x + 9) – (54 + x^3)`
`=x^3+27-54-x^3=-27`
`d,(2x + y) (4x^2 – 2xy + y^2) – (2x – y) (4x^2 + 2xy + y^2)`
`=8x^3+y^3-8x^3+y^3=2y^3`
`e,(a + b)^2 – (a – b)^2`
`=(a+b-a+b)(a+b+a-b)=2b.2a=4ab`
`f,(a + b)^3 – (a – b)^3 – 2b^3`
`=(a+b-a+b)[(a+b)^2+(a+b)(a-b)+(a-b)^2]-2b^3`
`=2b.(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)-2b^3`
`=2b.(3a^2+b^2)-2b^3=6a^2b+2b^3-2b^3`
`=6a^2b`
Đáp án:
Giải thích các bước giải:
a/ $(6x-2)^2+(2-5x)^2+2(6x-2)(2-5x)$
$=(6x-2+2-5x)^2$
$=x^2$
b/ $(2a^2+2a+1)(2a^2-2a+1)-(2a^2+1)^2$
$=(2a^2+1)^2-4a^2-(2a^2+1)^2$
$=-4a^2$
c/ $(x+3)(x^2-3x+9)-(54+x^3)$
$=x^3+27-54-x^3$
$=-27$
d/ $(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)$
$=8x^3+y^3-(8x^3-y^3)$
$=2y^3$
e/ $(a+b)^2-(a-b)^2$
$=(a+b+a-b)(a+b-a+b)$
$=2a.2b$
$=4ab$
f/ $(a+b)^3-(a-b)^3-2b^3$
$=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3$
$=6a^2b$
Chúc bạn học tốt !!