Tháng Năm 28, 2023

Rút gọn biểu thức: \(a)A = \left( {{x^2} – 3x + 9} \right)\left( {x + 3} \right) – \left( {54 + {x^3}} \right)\) \(b)B = {\left( {x – 1} \right)^2} + 2\left( {x – 1} \right)\left( {x + 1} \right) + {\left( {x + 1} \right)^2} + 5\) \(c)C = 9{x^2} – 2xy + \frac{1}{9}{y^2} – 2\left( {3x – \frac{1}{3}y} \right)\left( {3x + \frac{1}{3}y} \right) + {\left( {3x + \frac{1}{3}y} \right)^2}\)

Rút gọn biểu thức:

\(a)A = \left( {{x^2} – 3x + 9} \right)\left( {x + 3} \right) – \left( {54 + {x^3}} \right)\)

\(b)B = {\left( {x – 1} \right)^2} + 2\left( {x – 1} \right)\left( {x + 1} \right) + {\left( {x + 1} \right)^2} + 5\)

\(c)C = 9{x^2} – 2xy + \frac{1}{9}{y^2} – 2\left( {3x – \frac{1}{3}y} \right)\left( {3x + \frac{1}{3}y} \right) + {\left( {3x + \frac{1}{3}y} \right)^2}\)

A. \( a) 27\)

\( b) 4{x^2} + 8\)

\( c) \frac{4}{9}{y^2}\)

B. \( a) -27\)

\( b) 4{x^2} + 5\)

\( c) \frac{4}{9}{y^2}\)

C. \( a) 81\)

\( b) 4{x^2} + 5\)

\( c) -\frac{2}{3}{y^2}\)

D. \( a) -27\)

\( b) 4{x^2} + 5\)

\( c) \frac{2}{3}{y^2}\)

Hướng dẫn Chọn đáp án là: B

Lời giải chi tiết:

Hướng dẫn giải chi tiết

\(\begin{array}{l}a)\;A = \left( {{x^2} – 3x + 9} \right)\left( {x + 3} \right) – \left( {54 + {x^3}} \right)\\A = \left( {{x^2} – 3x + {3^2}} \right)\left( {x + 3} \right) – \left( {54 + {x^3}} \right)\\A = {x^3} + {3^3} – 54 – {x^3}\\A = 27 – 54 = – 27\end{array}\)

\(\begin{array}{l}b)\;B = {\left( {x – 1} \right)^2} + 2\left( {x – 1} \right)\left( {x + 1} \right) + {\left( {x + 1} \right)^2} + 5\\B = {\left( {\left( {x – 1} \right) + \left( {x + 1} \right)} \right)^2} + 5\\B = {\left( {x – 1 + x + 1} \right)^2} + 5\\B = {\left( {2x} \right)^2} + 5 = 4{x^2} + 5\end{array}\)

\(\begin{array}{l}c)\;C = 9{x^2} – 2xy + \frac{1}{9}{y^2} – 2\left( {3x + \frac{1}{3}y} \right)\left( {3x – \frac{1}{3}y} \right) + {\left( {3x + \frac{1}{3}y} \right)^2}\\C = {\left( {3x} \right)^2} – 2.3x.\frac{1}{3}y + {\left( {\frac{1}{3}y} \right)^2} – 2\left( {3x + \frac{1}{3}y} \right)\left( {3x – \frac{1}{3}y} \right) + {\left( {3x + \frac{1}{3}y} \right)^2}\\C = {\left( {3x – \frac{1}{3}y} \right)^2} – 2\left( {3x + \frac{1}{3}y} \right)\left( {3x – \frac{1}{3}y} \right) + {\left( {3x + \frac{1}{3}y} \right)^2}\\C = {\left( {\left( {3x – \frac{1}{3}y} \right) – \left( {3x + \frac{1}{3}y} \right)} \right)^2}\\C = {\left( {3x – \frac{1}{3}y – 3x – \frac{1}{3}y} \right)^2}\\C = {\left( { – \frac{2}{3}y} \right)^2} = \frac{4}{9}{y^2}\end{array}\)