May anh chi giup em giai bai nay voi

Giải thích các bước giải:

Ta có:

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