a,(x/3 – 1)^3 b,( -y^2 + 3x)^3 c,(x/y – 2y/x)^3 d,(x+3)^3 e,(1/2 – x)^3 f,(2x – y^2)^3 làm hằng đẳng thức nha 15/07/2021 Bởi Emery a,(x/3 – 1)^3 b,( -y^2 + 3x)^3 c,(x/y – 2y/x)^3 d,(x+3)^3 e,(1/2 – x)^3 f,(2x – y^2)^3 làm hằng đẳng thức nha
Đáp án: a,(x/3 – 1)^3=`(x/3)^3` -3.`(x/3)^2` +`3.1.3/x` -`1^3` = `x^3/27` – `x^2` + x-1 b,( -y^2 + 3x)^3=`((-y)^2)^3`+`3.((-y)^2)^2.3x+`3.(-y)^2`.`(3x)^2`+`(3x)^3` =`-y^6` + `9xy^4` – `27x^2y` + `27x^3` c,(x/y – 2y/x)^3=`(x/y)^3` – `3.(x/y)^2` . `((2y)/x)` + `3.x/y` . `((2y)/x)^2` – `((2y)/x)^3` = `x^3/y^3` – `(6x)/y` + `(12y)/x` – `(8y)^3/(x)^3` d,(x+3)^3=`x^3` + `3.x^2.3` + `3.x` . `3^2` + `3^3` =`x^3` + `9x^2` + `27x` + `27` e,(1/2 – x)^3=`(1/2)^3` – `3.(1/2)^2.x` + ` 3.1/2` . `x^2` – `x^3` =`1/8` – `12x` + `6x^2` – `x^3` f,(2x – y^2)^3=`(2x)^3 – 3.`(2x)^2` . `(-y)^2` + 3.`2x` . `((-y)^2)^2)` – `((y^2)^3)` =`8x^3` + `12x^2.y^2` – `6x.y^4` – `y^6` Bình luận
Đáp án:
a,(x/3 – 1)^3=`(x/3)^3` -3.`(x/3)^2` +`3.1.3/x` -`1^3`
= `x^3/27` – `x^2` + x-1
b,( -y^2 + 3x)^3=`((-y)^2)^3`+`3.((-y)^2)^2.3x+`3.(-y)^2`.`(3x)^2`+`(3x)^3`
=`-y^6` + `9xy^4` – `27x^2y` + `27x^3`
c,(x/y – 2y/x)^3=`(x/y)^3` – `3.(x/y)^2` . `((2y)/x)` + `3.x/y` . `((2y)/x)^2` – `((2y)/x)^3`
= `x^3/y^3` – `(6x)/y` + `(12y)/x` – `(8y)^3/(x)^3`
d,(x+3)^3=`x^3` + `3.x^2.3` + `3.x` . `3^2` + `3^3`
=`x^3` + `9x^2` + `27x` + `27`
e,(1/2 – x)^3=`(1/2)^3` – `3.(1/2)^2.x` + ` 3.1/2` . `x^2` – `x^3`
=`1/8` – `12x` + `6x^2` – `x^3`
f,(2x – y^2)^3=`(2x)^3 – 3.`(2x)^2` . `(-y)^2` + 3.`2x` . `((-y)^2)^2)` – `((y^2)^3)`
=`8x^3` + `12x^2.y^2` – `6x.y^4` – `y^6`