Đáp án:
\(\begin{array}{l}
1,\\
a,\,\,\,\,30x - 30\\
b,\,\,\,\, - 3{y^2}\\
2,\\
a,\,\,\, - x + 3\\
b,\,\,\,3
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
\left( {2x + 3} \right)\left( {5x - 10} \right) - 5x\left( {2x - 7} \right)\\
= 2x.\left( {5x - 10} \right) + 3.\left( {5x - 10} \right) - 5x\left( {2x - 7} \right)\\
= \left( {2x.5x - 2x.10} \right) + \left( {3.5x - 3.10} \right) - \left( {5x.2x - 5x.7} \right)\\
= \left( {10{x^2} - 20x} \right) + \left( {15x - 30} \right) - \left( {10{x^2} - 35x} \right)\\
= 10{x^2} - 20x + 15x - 30 - 10{x^2} + 35x\\
= \left( {10{x^2} - 10{x^2}} \right) + \left( { - 20x + 15x + 35x} \right) - 30\\
= 30x - 30\\
b,\\
\left( {5x - 3y} \right)\left( {2x + y} \right) - x\left( {10x - y} \right)\\
= 5x.\left( {2x + y} \right) - 3y.\left( {2x + y} \right) - x.\left( {10x - y} \right)\\
= \left( {5x.2x + 5x.y} \right) - \left( {3y.2x + 3y.y} \right) - \left( {x.10x - x.y} \right)\\
= \left( {10{x^2} + 5xy} \right) - \left( {6xy + 3{y^2}} \right) - \left( {10{x^2} - xy} \right)\\
= 10{x^2} + 5xy - 6xy - 3{y^2} - 10{x^2} + xy\\
= \left( {10{x^2} - 10{x^2}} \right) + \left( {5xy - 6xy + xy} \right) - 3{y^2}\\
= - 3{y^2}\\
2,\\
a,\\
\left( {x - 5} \right)\left( {2x + 3} \right) - 2x\left( {x - 3} \right) + 18\\
= x.\left( {2x + 3} \right) - 5.\left( {2x + 3} \right) - 2x.\left( {x - 3} \right) + 18\\
= \left( {x.2x + x.3} \right) - \left( {5.2x + 5.3} \right) - \left( {2x.x - 2x.3} \right) + 18\\
= \left( {2{x^2} + 3x} \right) - \left( {10x + 15} \right) - \left( {2{x^2} - 6x} \right) + 18\\
= 2{x^2} + 3x - 10x - 15 - 2{x^2} + 6x + 18\\
= \left( {2{x^2} - 2{x^2}} \right) + \left( {3x - 10x + 6x} \right) + \left( { - 15 + 18} \right)\\
= - x + 3\\
b,\\
\left( {12x - 5} \right)\left( {4x - 1} \right) + \left( {3x - 7} \right)\left( {1 - 16x} \right) - 83x + 5\\
= 12x.\left( {4x - 1} \right) - 5.\left( {4x - 1} \right) + 3x.\left( {1 - 16x} \right) - 7.\left( {1 - 16x} \right) - 83x + 5\\
= \left( {12x.4x - 12x.1} \right) - \left( {5.4x - 5.1} \right) + \left( {3x.1 - 3x.16x} \right) - \left( {7.1 - 7.16x} \right) - 83x + 5\\
= \left( {48{x^2} - 12x} \right) - \left( {20x - 5} \right) + \left( {3x - 48{x^2}} \right) - \left( {7 - 112x} \right) - 83x + 5\\
= 48{x^2} - 12x - 20x + 5 + 3x - 48{x^2} - 7 + 112x - 83x + 5\\
= \left( {48{x^2} - 48{x^2}} \right) + \left( { - 12x - 20x + 3x + 112x - 83x} \right) + \left( {5 - 7 + 5} \right)\\
= 3
\end{array}\)
Em xem lại đề bài 2a nhé!
