Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{\left( {x + 6} \right)^2} - {\left( {7 - x} \right)^2}\\
= \left[ {\left( {x + 6} \right) - \left( {7 - x} \right)} \right].\left[ {\left( {x + 6} \right) + \left( {7 - x} \right)} \right]\\
= \left[ {x + 6 - 7 + x} \right].\left[ {x + 6 + 7 - x} \right]\\
= \left( {2x - 1} \right).13\\
= 26x - 13\\
b,\\
{\left( {x + 4} \right)^2} + {\left( {x - 3} \right)^2} + x.\left( {x + 1} \right)\\
= \left( {{x^2} + 8x + 16} \right) + \left( {{x^2} - 6x + 9} \right) + \left( {{x^2} + x} \right)\\
= 3{x^2} + 3x + 25\\
c,\\
{\left( {x + 1} \right)^3} - {\left( {x - 2} \right)^3} + x.\left( {3{x^2} - 2x + 1} \right)\\
= \left( {{x^3} + 3{x^2} + 3x + 1} \right) - \left( {{x^3} - 6{x^2} + 12x - 8} \right) + \left( {3{x^3} - 2{x^2} + x} \right)\\
= {x^3} + 3{x^2} + 3x + 1 - {x^3} + 6{x^2} - 12x + 8 + 3{x^3} - 2{x^2} + x\\
= 3{x^3} + 7{x^2} - 8x + 9\\
2,\\
{175^2} + 625 - 50.175\\
= {175^2} + {25^2} - 2.25.175\\
= {175^2} - 2.175.25 + {25^2}\\
= {\left( {175 - 25} \right)^2}\\
= {150^2}
\end{array}\)
