Đáp án+Giải thích các bước giải:
1)
a) `A=(x-2)^2-2(x-2)(x+2)+4(x-1)^2`
`A=x^2-4x+4-2(x^2-4)+4(x^2-2x+1)`
`A=x^2-4x+4-2x^2+8+4x^2-8x+4`
`A=3x^2-12x+16`
b) Thay `x=-1/2` vào A có:
`A=3. (-1/2)^2-12. (-1/2)+16`
`A=3. 1/4 + 6+16`
`A=3/4+22`
`A=91/4`
Vậy `A=91/4` tại `x=-1/2.`
c) Để `A=16`
`<=>3x^2-12x+16=16`
`<=>3x^2-12x=0`
`<=>3x(x-4)=0`
`<=>x=0;x=4`
Vậy `x=0;x=4` thì `A=16.`
2)
a) `2xy(x^2y-5x+10y)`
`=2x^3 y^2-10x^2 y+10x y^2`
b) `(3x-5)(5+x^2)-3x(4/3 x^2+2x-3)`
`=15x+3x^3-25-5x^2-4x^3-6x^2+9x`
`=-x^3-11x^2+24x-25`
c) `3x(2x^2+x-1)+2x^2(1-3x)`
`=6x^3+3x^2-3x+2x^2-6x^3`
`=5x^2-3x`
3)
`a)(5x^2+2)^2`
`=(5x^2)^2+2.5x^2 .2+2^2`
`=25x^4+20x^2+4`
`b) (2x^2+1)(2x^2-1)`
`=(2x^2)^2 -1^2`
`=4x^4-1`
`c) (x^2y^2-z)^2`
`=(x^2 y^2)^2 - 2.x^2 y^2 .z +z^2`
`=x^4y^4-2z^2 y^2 z+z^2`
`d) y^2-4xy+4x^2`
`=y^2-2.y.2x +(2x)^2`
`=(y-2x)^2`
`e) 16x^4 - y^2`
`=(4x^2)^2-y^2`
`=(4x^2-y)(4x^2 +y)`
