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Đáp án+Giải thích các bước giải:
`1a)(4x+y)^2`
`=(4x)^2+2.4x.y+y^2`
`=16x^2+8xy+y^2`
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`b)(7x-8y)(7x+8y)`
`=(7x)^2-(8y)^2`
`=49x^2-64y^2`
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`c)52y^2-4x^2`
`=(5y)^2-(2x)^2`
`=(5y-2x)(5y+2x)`
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`d)(xyz-1)^2`
`=(xyz)^2-2xyz+1`
`=x^2y^2z^2-2xyz+1`
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`e)9x^2+6xy+y^2`
`=(3x)^2+2.3x.y+y^2`
`=(3x+y)^2`
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`2a)(x+1/2)(x-1/2)-x^2+1`
`=x^2-(1/2)^2-x^2+1`
`=1-1/4=3/4`
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`b)(3x+1)^2-(x-1)^2`
`=(3x+1-x+1)(3x+1+x-1)`
`=4x(2x+2)=8x^2+8x`
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`c)(x+3)^2+(2x+1)^2`
`=x^2+6x+9+4x^2+4x+1`
`=5x^2+10x+10`
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`3a)A=(x-y)(x^2+xy+y^2)`
`=x^3+x^2y+xy^2-x^2y-xy^2-y^3`
`=x^3-y^3`
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`b)x=2,y=1`
`=>A=2^3-1=8-1=7`
Vậy với `x=2,y=1` thì `A=7`.
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`4)x^2=(x+1)^2`
`<=>(x+1)^2-x^2=0`
`<=>(x+1-x)(x+1+x)=0`
`<=>1.(2x+1)=0`
`<=>2x+1=0`
`<=>2x=-1`
`<=>x=-1/2`
Vậy phương trình có nghiệm duy nhất `x=-1/2`.
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