Toán Lớp 8: Tính nhanh: 111^2-22×111+11^2
Rút gọn:a) (a-b)(a+c)(a^2+b^2)(a^4+b^4)
b) 2.(a+1)(a-1)+(a+1)^2+(a-1)^2
Giúp mình với ạ
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 8: Tính nhanh: 111^2-22×111+11^2
Rút gọn:a) (a-b)(a+c)(a^2+b^2)(a^4+b^4)
b) 2.(a+1)(a-1)+(a+1)^2+(a-1)^2
Giúp mình với ạ
Comments ( 1 )
{111^2} – 22.111 + {11^2}\\
= {111^2} – 2.111.11 + {11^2}\\
= {\left( {111 – 11} \right)^2}\\
= {100^2}\\
= 10000\\
a)\left( {a – b} \right)\left( {a + b} \right)\left( {{a^2} + {b^2}} \right)\left( {{a^4} + {b^4}} \right)\\
= \left( {{a^2} – {b^2}} \right)\left( {{a^2} + {b^2}} \right)\left( {{a^4} + {b^4}} \right)\\
= \left( {{a^4} – {b^4}} \right)\left( {{a^4} + {b^4}} \right)\\
= {a^8} – {b^8}\\
b)2\left( {a + 1} \right)\left( {a – 1} \right) + {\left( {a + 1} \right)^2} + {\left( {a – 1} \right)^2}\\
= {\left( {a + 1} \right)^2} + 2\left( {a + 1} \right)\left( {a – 1} \right) + {\left( {a – 1} \right)^2}\\
= {\left( {a + 1 + a – 1} \right)^2}\\
= {\left( {2a} \right)^2}\\
= 4{a^2}
\end{array}$