Đáp án:

\(\begin{array}{l}
11,\\
1)\,\,1\\
2)\,\,\, - 5\\
3)\,\,\, - 3\\
4)\,\,\, - 4\\
12,\\
1)\\
A = 7{x^2} - 17x\\
x =  - 1 \Rightarrow A = 24\\
2)\\
B = 2{x^2} + 16\\
x =  - 2 \Rightarrow B = 24\\
3)\\
C = 4x - 4\\
x = \dfrac{1}{4} \Rightarrow C =  - 3
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
11,\\
1)\,\,2{x^2}\left( {2 - 5x} \right) - 4{x^2} + 10{x^3} + 1\\
 = \left( {2{x^2}.2 - 2{x^2}.5x} \right) - 4{x^2} + 10{x^3} + 1\\
 = \left( {4{x^2} - 10{x^3}} \right) - 4{x^2} + 10{x^3} + 1\\
 = 4{x^2} - 10{x^3} - 4{x^2} + 10{x^3} + 1\\
 = \left( {4{x^2} - 4{x^2}} \right) + \left( { - 10{x^3} + 10{x^3}} \right) + 1\\
 = 1\\
2)\,\,\,3x\left( {x - 2} \right) - \left( {{x^2} - 6x + 5} \right) - 2{x^2}\\
 = \left( {3x.x - 3x.2} \right) - \left( {{x^2} - 6x + 5} \right) - 2{x^2}\\
 = 3{x^2} - 6x - {x^2} + 6x - 5 - 2{x^2}\\
 = \left( {3{x^2} - {x^2} - 2{x^2}} \right) + \left( { - 6x + 6x} \right) - 5\\
 =  - 5\\
3)\,\,\, - 4x\left( {2x - 1} \right) + 2x\left( {5x - 2} \right) - 2{x^2} - 3\\
 =  - \left( {4x.2x - 4x.1} \right) + \left( {2x.5x - 2x.2} \right) - 2{x^2} - 3\\
 =  - \left( {8{x^2} - 4x} \right) + \left( {10{x^2} - 4x} \right) - 2{x^2} - 3\\
 =  - 8{x^2} + 4x + 10{x^2} - 4x - 2{x^2} - 3\\
 = \left( { - 8{x^2} + 10{x^2} - 2{x^2}} \right) + \left( {4x - 4x} \right) - 3\\
 =  - 3\\
4)\,\,\,\left( {3x + 1} \right)\left( {3 - 2x} \right) - 7\left( {1 + x - {x^2}} \right) - {x^2}\\
 = \left( {3x.3 - 3x.2x + 1.3 - 1.2x} \right) - \left( {7 + 7x - 7{x^2}} \right) - {x^2}\\
 = \left( {9x - 6{x^2} + 3 - 2x} \right) - \left( {7 + 7x - 7{x^2}} \right) - {x^2}\\
 = 9x - 6{x^2} + 3 - 2x - 7 - 7x + 7{x^2} - {x^2}\\
 = \left( { - 6{x^2} + 7{x^2} - {x^2}} \right) + \left( {9x - 2x - 7x} \right) + \left( {3 - 7} \right)\\
 =  - 4\\
12,\\
1)\\
A = 4{x^2} - 2x + 3x\left( {x - 5} \right)\\
 = 4{x^2} - 2x + 3x.x - 3x.5\\
 = 4{x^2} - 2x + 3{x^2} - 15x\\
 = 7{x^2} - 17x\\
x =  - 1 \Rightarrow A = 7.{\left( { - 1} \right)^2} - 17.\left( { - 1} \right) = 7 + 17 = 24\\
2)\\
B = 3x\left( {x - 2} \right) - \left( {x + 2} \right)\left( {x - 8} \right)\\
 = \left( {3x.x - 3x.2} \right) - \left( {x.x - x.8 + 2.x - 2.8} \right)\\
 = \left( {3{x^2} - 6x} \right) - \left( {{x^2} - 8x + 2x - 16} \right)\\
 = 3{x^2} - 6x - {x^2} + 8x - 2x + 16\\
 = \left( {3{x^2} - {x^2}} \right) + \left( { - 6x + 8x - 2x} \right) + 16\\
 = 2{x^2} + 16\\
x =  - 2 \Rightarrow B = 2.{\left( { - 2} \right)^2} + 16 = 8 + 16 = 24\\
3)\\
C = \left( {x - 1} \right)\left( {2x + 1} \right) - \left( {x - 1} \right)\left( {2x - 3} \right)\\
 = \left( {x - 1} \right).\left[ {\left( {2x + 1} \right) - \left( {2x - 3} \right)} \right]\\
 = \left( {x - 1} \right).\left( {2x + 1 - 2x + 3} \right)\\
 = \left( {x - 1} \right).4\\
 = 4x - 4\\
x = \dfrac{1}{4} \Rightarrow C = 4.\dfrac{1}{4} - 4 = 1 - 4 =  - 3
\end{array}\)

Đáp án:

11,1)12)−53)−34)−412,1)A=7x2−17xx=−1⇒A=242)B=2x2+16x=−2⇒B=243)C=4x−4x=14⇒C=−3

Giải thích các bước giải:

11,1)12)−53)−34)−412,1)A=7x2−17xx=−1⇒A=242)B=2x2+16x=−2⇒B=243)C=4x−4x=14⇒C=−3Giải thích các bước giải:Ta có:11,1)2x2(2−5x)−4x2+10x3+1=(2x2.2−2x2.5x)−4x2+10x3+1=(4x2−10x3)−4x2+10x3+1=4x2−10x3−4x2+10x3+1=(4x2−4x2)+(−10x3+10x3)+1=12)3x(x−2)−(x2−6x+5)−2x2=(3x.x−3x.2)−(x2−6x+5)−2x2=3x2−6x−x2+6x−5−2x2=(3x2−x2−2x2)+(−6x+6x)−5=−53)−4x(2x−1)+2x(5x−2)−2x2−3=−(4x.2x−4x.1)+(2x.5x−2x.2)−2x2−3=−(8x2−4x)+(10x2−4x)−2x2−3=−8x2+4x+10x2−4x−2x2−3=(−8x2+10x2−2x2)+(4x−4x)−3=−34)(3x+1)(3−2x)−7(1+x−x2)−x2=(3x.3−3x.2x+1.3−1.2x)−(7+7x−7x2)−x2=(9x−6x2+3−2x)−(7+7x−7x2)−x2=9x−6x2+3−2x−7−7x+7x2−x2=(−6x2+7x2−x2)+(9x−2x−7x)+(3−7)=−412,1)A=4x2−2x+3x(x−5)=4x2−2x+3x.x−3x.5=4x2−2x+3x2−15x=7x2−17xx=−1⇒A=7.(−1)2−17.(−1)=7+17=242)B=3x(x−2)−(x+2)(x−8)=(3x.x−3x.2)−(x.x−x.8+2.x−2.8)=(3x2−6x)−(x2−8x+2x−16)=3x2−6x−x2+8x−2x+16=(3x2−x2)+(−6x+8x−2x)+16=2x2+16x=−2⇒B=2.(−2)2+16=8+16=243)C=(x−1)(2x+1)−(x−1)(2x−3)=(x−1).[(2x+1)−(2x−3)]=(x−1).(2x+1−2x+3)=(x−1).4=4x−4x=14⇒C=4.14−4=1−4=−3