Đáp án+Giải thích các bước giải:
Bài `1:`
`a) (x+1)^2+(x-2)(x+2)-3(x+1)`
`=x^2+2x+1+x^2-4 -3x-3`
`=(x^2+x^2)+(2x-3x)+(1-3-4)`
`= 2x^2 - x - 6`
`b) (3x+1)^2+2(3x+1)(2x-1)+(2x-1)^2`
`=[(3x+1)+(2x-1)]^2`
`=(3x+1+2x-1)^2`
`=(5x)^2`
`=25x^2`
Bài `2:`
`a) (x+3)^3-x(3x+1)^2+(2x+1)(4x^2-2x+1)=28`
`<=> x^3 + 9x^2 + 27x + 27 -x(9x^2+6x+1)+(2x)^3+1=28`
`<=> x^3 + 9x^2 + 27x + 27 - 9x^3 -6x^2-x+8x^3+1=28`
`<=> (x^3-9x^3+8x^3)+(9x^2-6x^2)+(27x-x)=28-1-27`
`<=>3x^2+ 26x = 0`
`<=> x(3x+26)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\3x+26=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\3x=-26\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{-26}{3}\end{array} \right.\)
`b) (2x-1)^2+(x+3)^2-5(x+7)(x-7)=15`
`<=> 4x^2 - 4x + 1 +x^2 + 6x + 9 -5(x^2-49)=15`
`<=> 5x^2+2x+10 - 5x^2+245=15`
`<=> (5x^2-5x^2)+2x=15-245-10`
`<=> 2x = -240`
`<=> x = -120`
Vậy `x=-120`
