Đáp án:
$\begin{array}{l}
3a){\left( {x + y} \right)^2} - {\left( {x - y} \right)^2}\\
= \left( {x + y + x - y} \right)\left( {x + y - x + y} \right)\\
= 2x.2y\\
= 4xy\\
b){\left( {3x + 1} \right)^2} - {\left( {x + 1} \right)^2}\\
= \left( {3x + 1 + x + 1} \right)\left( {3x + 1 - x - 1} \right)\\
= \left( {4x + 2} \right).\left( {2x} \right)\\
= 4x.\left( {2x + 1} \right)\\
c){x^3} + {y^3} + {z^3} - 3xyz\\
= {\left( {x + y} \right)^3} - 3xy\left( {x + y} \right) + {z^3} - 3xyz\\
= {\left( {x + y} \right)^3} + {z^3} - 3xy\left( {x + y + z} \right)\\
= \left( {x + y + z} \right)\left[ {{{\left( {x + y} \right)}^2} - \left( {x + y} \right)z + {z^2}} \right]\\
- 3xy\left( {x + y + z} \right)\\
= \left( {x + y + z} \right)\left[ {{x^2} + 2xy + {y^2} - xz - yz + {z^2} - 3xy} \right]\\
= \left( {x + y + z} \right)\left[ {{x^2} + {y^2} + {z^2} - xz - yz - xy} \right]\\
4)\\
a){25^2} - {15^2}\\
= \left( {25 - 15} \right)\left( {25 + 15} \right)\\
= 10.40\\
= 400\\
b){87^2} + {73^2} - {27^2} - {13^2}\\
= \left( {{{87}^2} - {{13}^2}} \right) + \left( {{{73}^2} - {{27}^2}} \right)\\
= \left( {87 + 13} \right)\left( {87 - 13} \right) + \left( {73 - 27} \right)\left( {73 + 27} \right)\\
= 100.74 + 46.100\\
= 100.\left( {74 + 46} \right)\\
= 100.120\\
= 12000
\end{array}$
