Đáp án:
\(\begin{array}{l}
1,\\
a,\,\,\,{\left( {x - 3} \right)^2}\\
b,\,\, - {\left( {x - 5} \right)^2}\\
2,\\
a,\,\,\,2800\\
b,\,\,\,300\\
c,\,\,\,325
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\,\,\,{x^2} - 6x + 9 = {x^2} - 2.x.3 + {3^2} = {\left( {x - 3} \right)^2}\\
b,\,\,10x - 25 - {x^2} = - \left( {{x^2} + 25 - 10x} \right) = - \left( {{x^2} - 10x + 25} \right)\\
= - \left( {{x^2} - 2.x.5 + {5^2}} \right) = - {\left( {x - 5} \right)^2}\\
2,\\
a,\,\,\,{55^2} - {15^2} = \left( {55 + 15} \right).\left( {55 - 15} \right) = 70.40 = 2800\\
b,\,\,\,37,5.6,5 - 7,5.3,4 - 6,6.7,5 + 3,5.37,5\\
= \left( {37,5.6,5 + 3,5.37,5} \right) - \left( {7,5.3,4 + 6,6.7,5} \right)\\
= 37,5.\left( {6,5 + 3,5} \right) - 7,5.\left( {3,4 + 6,6} \right)\\
= 37,5.10 - 7,5.10\\
= 375 - 75\\
= 300\\
c,\,\,\,{95^2} + {60^2} - 120.95 - {30^2}\\
= \left( {{{95}^2} - 120.95 + {{60}^2}} \right) - {30^2}\\
= \left( {{{95}^2} - 2.95.60 + {{60}^2}} \right) - {30^2}\\
= {\left( {95 - 60} \right)^2} - {30^2}\\
= {35^2} - {30^2}\\
= \left( {35 - 30} \right).\left( {35 + 30} \right)\\
= 5.65\\
= 325
\end{array}\)
