Đáp án:
\(\begin{array}{l}
7,\\
G = - 4y + 5\\
8,\\
I = {x^3} - 7{x^2} + 18x - 25\\
9,\\
K = 15{x^2} + 75x\\
10,\\
M = 12{a^2} + 3a + 8\\
11,\\
N = - 18{x^2} - 54\\
12,\\
H = - 2{y^3}\\
13,\\
P = {x^6} - 64
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
7,\\
G = {\left( {y - 2} \right)^2} - \left( {y + 1} \right)\left( {y - 1} \right)\\
= \left( {{y^2} - 2.y.2 + {2^2}} \right) - \left( {{y^2} - {1^2}} \right)\\
= \left( {{y^2} - 4y + 4} \right) - \left( {{y^2} - 1} \right)\\
= {y^2} - 4y + 4 - {y^2} + 1\\
= - 4y + 5\\
8,\\
I = {\left( {x - 2} \right)^3} - \left( {x + 1} \right)\left( {x - 1} \right) + 6.\left( {x - 3} \right)\\
= \left( {{x^3} - 3.{x^2}.2 + 3.x{{.2}^2} - {2^3}} \right) - \left( {{x^2} - {1^2}} \right) + \left( {6x - 18} \right)\\
= \left( {{x^3} - 6{x^2} + 12x - 8} \right) - \left( {{x^2} - 1} \right) + 6x - 18\\
= {x^3} - 6{x^2} + 12x - 8 - {x^2} + 1 + 6x - 18\\
= {x^3} + \left( { - 6{x^2} - {x^2}} \right) + \left( {12x + 6x} \right) + \left( { - 8 + 1 - 18} \right)\\
= {x^3} - 7{x^2} + 18x - 25\\
9,\\
K = {\left( {x + 5} \right)^3} - {x^3} - 125\\
= \left( {{x^3} + 3.{x^2}.5 + 3.x{{.5}^2} + {5^3}} \right) - {x^3} - 125\\
= \left( {{x^3} + 15{x^2} + 75x + 125} \right) - {x^3} - 125\\
= {x^3} + 15{x^2} + 75x + 125 - {x^3} - 125\\
= 15{x^2} + 75x\\
10,\\
M = {\left( {a + 2} \right)^3} - a.{\left( {a - 3} \right)^2}\\
= \left( {{a^3} + 3.{a^2}.2 + 3.a{{.2}^2} + {2^3}} \right) - a.\left( {{a^2} - 2.a.3 + {3^2}} \right)\\
= \left( {{a^3} + 6{a^2} + 12a + 8} \right) - a.\left( {{a^2} - 6a + 9} \right)\\
= {a^3} + 6{a^2} + 12a + 8 - {a^3} + 6{a^2} - 9a\\
= \left( {{a^3} - {a^3}} \right) + \left( {6{a^2} + 6{a^2}} \right) + \left( {12a - 9a} \right) + 8\\
= 12{a^2} + 3a + 8\\
11,\\
N = {\left( {x - 3} \right)^3} - {\left( {x + 3} \right)^3}\\
= \left( {{x^3} - 3.{x^2}.3 + 3.x{{.3}^2} - {3^3}} \right) - \left( {{x^3} + 3.{x^2}.3 + 3.x{{.3}^2} + {3^3}} \right)\\
= \left( {{x^3} - 9{x^2} + 27x - 27} \right) - \left( {{x^3} + 9{x^2} + 27x + 27} \right)\\
= {x^3} - 9{x^2} + 27x - 27 - {x^3} - 9{x^2} - 27x - 27\\
= \left( {{x^3} - {x^3}} \right) + \left( { - 9{x^2} - 9{x^2}} \right) + \left( {27x - 27x} \right) + \left( { - 27 - 27} \right)\\
= - 18{x^2} - 54\\
12,\\
H = \left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right) - \left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right)\\
= \left( {x - y} \right).\left( {{x^2} + x.y + {y^2}} \right) - \left( {x + y} \right).\left( {{x^2} - x.y + {y^2}} \right)\\
= \left( {{x^3} - {y^3}} \right) - \left( {{x^3} + {y^3}} \right)\\
= {x^3} - {y^3} - {x^3} - {y^3}\\
= - 2{y^3}\\
13,\\
P = \left( {x - 2} \right)\left( {{x^2} - 2x + 4} \right)\left( {x + 2} \right)\left( {{x^2} + 2x + 4} \right)\\
= \left[ {\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)} \right].\left[ {\left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right)} \right]\\
= \left[ {\left( {x - 2} \right).\left( {{x^2} + x.2 + {2^2}} \right)} \right].\left[ {\left( {x + 2} \right)\left( {{x^2} - x.2 + {2^2}} \right)} \right]\\
= \left( {{x^3} - {2^3}} \right).\left( {{x^3} + {2^3}} \right)\\
= \left( {{x^3} - 8} \right)\left( {{x^3} + 8} \right)\\
= {\left( {{x^3}} \right)^2} - {8^2}\\
= {x^6} - 64
\end{array}\)
