\(a,\left(x+2\right)\left(3x+2\right)-\left(3x-1\right)\left(x-5\right)=11\\ \Leftrightarrow\left(3x^2+6x+2x+4\right)-\left(3x^2-15x-x+5\right)=11\\ \Leftrightarrow3x^2+8x+4-3x^2+16x-5=11\\ \Leftrightarrow24x-1=11\\ \Leftrightarrow24x=11+1=12\\ \Leftrightarrow x=\dfrac{12}{24}=\dfrac{1}{2}\\ b,2\left(2x+1\right)\left(8x-3\right)+\left(3-4x\right)\left(8x-7\right)=6x+73\\ \Leftrightarrow\left(4x+2\right)\left(8x-3\right)-\left(4x-3\right)\left(8x-7\right)=6x+73\\ \Leftrightarrow\left(32x^2-12x+16x-6\right)-\left(32x^2-28x-24x+21\right)=6x+73\\ \Leftrightarrow32x^2+4x-6-32x^2+52x-21=6x+73\\ \Leftrightarrow56x-27=6x+73\\ \Leftrightarrow56x-6x=73+27\\ \Leftrightarrow50x=100\\ \Leftrightarrow x=\dfrac{100}{50}\\ \Leftrightarrow x=2\)
Câu `1`
`a,(x+2)*(3x+2)-(3x-1)*(x-5)=11`
`=> 3x^2 + 8x + 4 - (3x^2 - 16x + 5 )=11`
`=> 3x^2 + 8x + 4 - 3x^2 + 16x - 5 = 11`
`=> 24x - 1 =11`
`=> 24x = 12`
`=> x=1/2`
Vậy: `x=1/2`
`b, 2(2x + 1)(8x - 3) + (3 - 4x)(8x - 7) = 6x + 73`
`=> 32x^2 + 4x - 6 - 32x^2 + 52x - 21 = 6x + 73`
`=> 56x - 27 = 6x + 73`
`=> 56x - 6x = 73 + 27`
`=> 50x = 100`
`=> x=2`
Vậy: `x=2`
Câu `2`
`(x^3-x+1)(2x+1)+(x+1)(x-2)`
`= 2x^4 + x^3 - 2x^2 + 1 + x^2- x -2`
`= 2x^4 + x^3 + (-2x^2 + x^2) -x + (1 - 2)`
`= 2x^4 + x^3 - x^2 - x - 1`
`b, (2x + 5)(2x - 3)-5(x+3)`
`= 4x^2 + 4x - 15 - 5x - 15`
`= 4x^2 + (4x - 5x) + (-15 - 15)`
`= 4x^2 - x - 30`
Bài 1:
a)
\[
(x+2)(3x+2) - (3x-1)(x-5) = 11
\]
\[
(x+2)(3x+2) = 3x^2 + 2x + 6x + 4 = 3x^2 + 8x + 4
\]
\[
(3x-1)(x-5) = 3x^2 - 15x - x + 5 = 3x^2 - 16x + 5
\]
\[
3x^2 + 8x + 4 - (3x^2 - 16x + 5) = 11
\]
\[
3x^2 + 8x + 4 - 3x^2 + 16x - 5 = 11
\]
\[
24x - 1 = 11
\]
\[
24x = 12 \quad \Rightarrow \quad x = \frac{12}{24} = \frac{1}{2}
\]
b)
\[
2(2x+1)(8x-3) + (3-4x)(8x-7) = 6x + 73
\]
\[
2(2x+1)(8x-3) = 2(16x^2 - 6x + 8x - 3) = 32x^2 + 4x - 6
\]
\[
(3-4x)(8x-7) = 24x - 32x^2 - 21 + 28x = -32x^2 + 52x - 21
\]
\[
32x^2 + 4x - 6 - 32x^2 + 52x - 21 = 6x + 73
\]
\[
56x - 27 = 6x + 73
\]
\[
50x = 100 \quad \Rightarrow \quad x = \frac{100}{50} = 2
\]
Bài 2:
a)
\[
(x^3 - x + 1)(2x + 1) = 2x^4 + x^3 - 2x^2 - x + 2x + 1 = 2x^4 + x^3 - 2x^2 + 1
\]
\[
(x + 1)(x - 2) = x^2 - 2x + x - 2 = x^2 - x - 2
\]
\[
A = 2x^4 + x^3 - 2x^2 + 1 + x^2 - x - 2 = 2x^4 + x^3 - x^2 - x - 1
\]
b)
\[
(2x + 5)(2x - 3) = 4x^2 - 6x + 10x - 15 = 4x^2 + 4x - 15
\]
\[
5(x + 3) = 5x + 15
\]
\[
B = 4x^2 + 4x - 15 - 5x - 15 = 4x^2 - x - 30
\]