Đáp án:
\(\begin{array}{l}
A = 8\\
B = - 22\\
C = - 76
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \left( {x + 4} \right)\left( {x + 2} \right) - x\left( {x + 6} \right)\\
= \left( {{x^2} + 2x + 4x + 8} \right) - \left( {{x^2} + 6x} \right)\\
= \left( {{x^2} + 6x + 8} \right) - \left( {{x^2} + 6x} \right)\\
= {x^2} + 6x + 8 - {x^2} - 6x\\
= 8\\
B = \left( {x - 5} \right)\left( {2x + 3} \right) - 2x\left( {x - 3} \right) + x + 7\\
= \left( {2{x^2} + 3x - 10x - 15} \right) - \left( {2{x^2} - 6x} \right) + x + 7\\
= \left( {2{x^2} - 7x - 15} \right) - \left( {2{x^2} - 6x} \right) + x + 7\\
= 2{x^2} - 7x - 15 - 2{x^2} + 6x + x - 7\\
= \left( {2{x^2} - 2{x^2}} \right) + \left( { - 7x + 6x + x} \right) + \left( { - 15 - 7} \right)\\
= - 22\\
C = \left( {3x - 5} \right)\left( {2x + 11} \right) - \left( {3x + 7} \right)\left( {2x + 3} \right)\\
= \left( {6{x^2} + 33x - 10x - 55} \right) - \left( {6{x^2} + 9x + 14x + 21} \right)\\
= \left( {6{x^2} + 23x - 55} \right) - \left( {6{x^2} + 23x + 21} \right)\\
= 6{x^2} + 23x - 55 - 6{x^2} - 23x - 21\\
= \left( {6{x^2} - 6{x^2}} \right) + \left( {23x - 23x} \right) + \left( { - 55 - 21} \right)\\
= - 76
\end{array}\)
