Toán học 20 Tháng Hai, 2023 No Comments By Thúy Hường Toán Lớp 8: 1_ Tính a) (2x^2+1/3)^3 b)(x^2+2y^2)^2 c)(2/3x+y^2)^2 đ)(3x^2-5y)^2
Giải đáp: $\begin{array}{l}a){\left( {2{x^2} + \dfrac{1}{3}} \right)^3}\\ = {\left( {2{x^2}} \right)^3} + 3.{\left( {2{x^2}} \right)^2}.\dfrac{1}{3} + 3.2{x^2}.\dfrac{1}{9} + \dfrac{1}{{27}}\\ = 8{x^6} + 4{x^4} + \dfrac{2}{3}{x^2} + \dfrac{1}{{27}}\\b){\left( {{x^2} + 2{y^2}} \right)^2}\\ = {x^4} + 4{x^2}{y^2} + 4{y^4}\\c){\left( {\dfrac{2}{3}x + {y^2}} \right)^2}\\ = \dfrac{4}{9}{x^2} + \dfrac{4}{3}x{y^2} + {y^4}\\d){\left( {3{x^2} – 5y} \right)^2}\\ = 9{x^4} – 30{x^2}y + 25{y^2}\end{array}$ Trả lời
a){\left( {2{x^2} + \dfrac{1}{3}} \right)^3}\\
= {\left( {2{x^2}} \right)^3} + 3.{\left( {2{x^2}} \right)^2}.\dfrac{1}{3} + 3.2{x^2}.\dfrac{1}{9} + \dfrac{1}{{27}}\\
= 8{x^6} + 4{x^4} + \dfrac{2}{3}{x^2} + \dfrac{1}{{27}}\\
b){\left( {{x^2} + 2{y^2}} \right)^2}\\
= {x^4} + 4{x^2}{y^2} + 4{y^4}\\
c){\left( {\dfrac{2}{3}x + {y^2}} \right)^2}\\
= \dfrac{4}{9}{x^2} + \dfrac{4}{3}x{y^2} + {y^4}\\
d){\left( {3{x^2} – 5y} \right)^2}\\
= 9{x^4} – 30{x^2}y + 25{y^2}
\end{array}$