Advertisements (Quảng cáo)
Rút gọn các biểu thức:
a. \(P = {\left( {5x – 1} \right)^2} + 2\left( {1 – 5x} \right)\left( {4 + 5x} \right) + {\left( {5x + 4} \right)^2}\)
b. \(Q = {\left( {x – y} \right)^3} + {\left( {y + x} \right)^3} + {\left( {y – x} \right)^3} – 3xy\left( {x + y} \right)\)
a. \(P = {\left( {5x – 1} \right)^2} + 2\left( {1 – 5x} \right)\left( {4 + 5x} \right) + {\left( {5x + 4} \right)^2}\)
Advertisements (Quảng cáo)
\(\eqalign{ & = {\left( {1 – 5x} \right)^2} + 2\left( {1 – 5x} \right)\left( {5x + 4} \right) + {\left( {5x + 4} \right)^2} \cr & = {\left[ {\left( {1 – 5x} \right) + \left( {5x + 4} \right)} \right]^2} = {5^2} = 25 \cr} \)
b. \(Q = {\left( {x – y} \right)^3} + {\left( {y + x} \right)^3} + {\left( {y – x} \right)^3} – 3xy\left( {x + y} \right)\)
\(\eqalign{ & = {x^3} – 3{x^2}y + 3x{y^2} – {y^3} + {y^3} + 3x{y^2} + 3{x^2}y + {x^3} + {y^3} – 3x{y^2} + 3{x^2}y \cr & – {x^3} – 3{x^2}y – 3x{y^2} = {x^3} + {y^3} \cr} \)