câu 1: (2x + 1)^3 – (2x + 1) . (4x^2 – 2x +1) – 3 . (2x – 1)^2 = 15 câu 2: y . (y + 3)^2 – (y + 2) . (y^2 – 2y + 4) – 6 . (y + 5) . (y – 5) = 97

Đáp án:

 $1)
x=1\\
2)
y=-5\\
3)
x=\dfrac{1}{5}\\
4)
x=7$

Giải thích các bước giải:

 $1)
(2x+1)^3-(2x+1)(4x^2-2x+1)-3(2x-1)^2=15\\
\Leftrightarrow 8x^3+3.(2x)^2.1+3.2x.1^2+1-(8x^3+1)-3(4x^2-4x+1)=15\\
\Leftrightarrow 8x^3+12x^2+6x+1-8x^3-1-12x^3+12x-3=15\\
\Leftrightarrow 18x=15+3\\
\Leftrightarrow x=\dfrac{18}{18}=1\\
2)
y(y+3)^2-(y+2)(y^2-2y+4)-6.(y+5)(y-5)=97\\
\Leftrightarrow y(y^2+6y+9)-(y^3+8)-6(y^2-25)=97\\
\Leftrightarrow y^3+6y^2+9y-y^3-8-6y^2+150=97\\
\Leftrightarrow 9y+142=97\\
\Leftrightarrow 9y=97-142=-45\\
\Leftrightarrow y=-5\\
3)
(x-3)^3-(x-3)(x^2+3x+9)+9.(x+1)^2=18\\
\Leftrightarrow x^3-3.x^2.3+3.x.3^2-3^3-(x^3-27)+9(x^2+2x+1)=18\\
\Leftrightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=18\\
\Leftrightarrow 45x+9=18\\
\Leftrightarrow 45x=18-9=9\\
\Leftrightarrow x=\dfrac{9}{45}=\dfrac{1}{5}\\
4)
x(x-4)(x+4)-(x-5)(x^2+5x+25)=13\\
\Leftrightarrow x(x^2-16)-(x^3-5^3)=13\\
\Leftrightarrow x^3-16x-x^3+125=13\\
\Leftrightarrow -16x+125=13\\
\Leftrightarrow -16x=13-125=-112\\
\Leftrightarrow x=\dfrac{-112}{-16}=7$