Đáp án:
`1)(2x+3)³`
`=(2x)³+3.(2x)².3+3.2x.3²+3³`
`=8x³+36x²+54x+27`
`2)(x+1/3)³`
`=x³+3.x². 1/3+3.x. (1/3)²+(1/3)³`
`=x³+x²+1/3x+1/27`
`3)(2x+y)³`
`=(2x)³+3.(2x)².y+3.2x.y²+y³`
`=8x³+12x²y+6xy²+y³`
`4)(2x+1/3)³`
`=(2x)³+3.(2x)². 1/3+3.2x. (1/3)²+(1/3)³`
`=8x³+4x²+2/3x+1/27`
`5)(2x+4)³`
`=(2x)³+3.(2x)².4+3.2x.4²+4³`
`=8x³+48x²+96x+64`
`6)(x+3)³`
`=x³+3.x².3+3.x.3²+3³`
`=x³+9x²+27x+27`
`7)(x+y)³=x³+3x²y+3xy²+y³`
`8)(x+1)³=x³+3x²+3x+1`
`9)(2x+3y)³`
`=(2x)³+3.(2x)².3y+3.2x.(3y)²+(3y)³`
`=8x³+36x²y+54xy²+27y³`
`10)(2x+1/5)³`
`=(2x)³+3.(2x)². 1/5+3.2x. (1/5)²+(1/5)³`
`=8x³+12/5x²+6/25x+1/125`
`11)(3x+1)³`
`=(3x)³+3.(3x)².1+3.3x.1²+1³`
`=27x³+27x²+9x+1`
`12)(3x+y²)³`
`=(3x)³+3.(3x)².y²+3.3x.(y²)²+(y²)³`
`=27x³+27x²y²+9xy^4+y^6`
`13)(1/(y²)+y/x)³`
`=(1/(y²))³+3. (1/(y²))² . y/x+3. 1/(y²) . (y/x)²+(y/x)³`
`=1/(y^6)+3/(xy³)+3/(x²)+(y³)/(x³)`
`14)(x/y+1)³`
`=(x/y)³+3. (x/y)².1+3. x/y . 1²+1³`
`=(x³)/(y³)+(3x²)/(y²)+(3x)/y+1`
`15)(x/2+y)³`
`=(x/2)³+3. (x/2)² .y+3. x/2 . y²+y³`
`=(x³)/8+3/4x²y+3/2xy²+y³`
Giải thích các bước giải:
Áp dụng:Hằng đẳng thức Lập phương của một tổng:
`(A+B)³=A³+3A²B+3AB²+B³`
